(Describer) Titles: Welcome to Algebra 1: Factoring Trinomials with a Leading Coefficient Not Equal to 1.

Hi, guys.
Welcome to Algebra 1.
Today's lesson will focus on
factoring trinomials
when your leading
coefficient is not 1.
What you know about
factoring trinomials
with a leading coefficient
of 1
will help you get through
these problems.
You ready? Let's go.

(Describer) On screen, x-squared plus 5x plus 6.

Okay,
so to jog your memory,
let's first think back about
how you would factor
this trinomial, for example.
You'd probably start out
by setting up what the answer
is going to look like:
with your sets
of parentheses.
You know you'll have
some X's out front,
like that.

(Describer) She writes on the screen.

Then you need
the factors of 6.
I know 1 times 6
will give me 6,
and so will 2 times 3.
And I need the pair
of factors that,
in this case,
will combine to give me 5.
So when I combine 1 and 6,
I get 7.
That's not the pair.
2 and 3, when I combine those,
I get 5.
That is the pair
that I want.
I'd say my factors
are X plus 2, and X plus 3.
Here, we factored a trinomial
that had a leading
coefficient of 1.
There's an invisible 1 there,
for that first term.
What happens when you have
something like this?

(Describer) Three x-squared plus 10x plus 8.

(female narrator)
3X squared plus 10X plus 8.
When you have a trinomial
and the leading coefficient
is not 1?
To handle these types
of problems,
there's a few steps
you should learn,
then we'll return
to that problem.
There's a few; there's five.
The first thing
to remember,
looking at the top,
is your trinomial
is written in the form
AX squared plus BX plus C.
The first step is multiplying
the A and the C.
Then figure out the factors
of that product
that will add up to give us B,
that middle number,
like you were doing before.
Then we'll do something called
splitting the middle term.
I'll show you
what I mean by that.
Then we're going to factor
our two binomials,
and then we'll have our answer.
Keep these steps written
on the side
to follow along while
we factor this trinomial.
The first thing I do is,
I know this trinomial
is written
in the form AX squared
plus BX plus C.
You need to first factor
the A and the C,
or the first number
and the last number.
You need to multiply
those together, I'm sorry.
So 3 times 8...
that's 24, right?
So I've found the product
of A and C.
Now I need to figure out
what factors of 24
would also combine
and give me 10?
This step we've
handled before,
as far as listing our factors
and figuring out
the right sum.
In this problem,
there's an extra step
of multiplying that A and
that C together,
to start with.
Now that we've got 24,
let's list our factors.
So 1 and 24;
2 and 12;
3 and 8; and 4 and 6.
All those pairs will make 24
when you multiply them.
Now I need to figure out
which pair of factors
would give me a sum of 10?
Let's start testing these out.
Combining 1 and 24,
that's 25.
2 and 12, that's 14.
3 and 8, that's 11.
4 and 6, that is 10,
right?
So these 3 didn't work,
but the 4 and the 6 did work.
Now what I'm going to do,
I'm going to bring this off
to the side of it.
Let's erase this.
I'm at the point now
where I split the middle term.
What that means is that
instead of writing--
this is my middle term,
that 10X.
I'm going to split it,
so instead of writing 10X,
I'm going to write it
as a sum of two other terms.
I'll split it into two terms.
So I'll still have
the 3X squared,
but instead of writing 10X,
I'm going to write
4X plus 6X--
going back over here
to our factors--
because 4 and 6,
I know will add to give me 10.
So 4X plus 6X gives me 10X.
You're not changing
the meaning of the problem,
you're just representing
that 10X differently.
Not 64X,
because that would change
the meaning of your problem--
it's 6X.
There we go, plus 8.
So like I said, 10X,
we're just representing it
as 4X plus 6X,
because that is still 10X.
We're doing this just
to get through this problem.
Let me get this
out of our way.
Now, what we do
is we look at this
like it's two
different binomials.
Like we have this first group,
right here,
and then we have
the second group, right here.
And we'll factor
this first group,
and then we'll factor
the second group.
Remember, when we factored
binomials,
we were looking for our
greatest common factor, right?
Between 3X squared and 4X.
First, just consider
your 3 and your 4.
There's no factors
that 3 and 4
have in common,
except 1, right?
So I can just keep that
in my mind.
Now, 8 squared and X--
you may need to see this.
Let's go ahead
and work to the side.
We may soon
not need to write it.
So factor in that 3--
1 and 3, I know, right?
It's prime,
so that's it for 3.
Then factoring X squared,
you know you have X and X,
and that's it
for 3X squared.
Now, factoring 4X,
I know 1 times 4
would give me 4,
and so would 2 times 2.
And then I do have one factor
of X that I can write.
When I need the greatest
common factor--
in this case, all they have
in common is a 1--
that doesn't change anything,
really--and the X.
I'll say, all right,
the greatest common factor
of those two terms is X.
I'll write my X,
open up my parentheses,
then I need to divide
each of those terms by X.
So 3X squared divided by X.
That's like an invisible 1
I don't see.
So that's like 3 divided by 1,
which is 3.
Then X squared
divided by X to the 1st,
so subtracting
your exponents,
that's just X to the first.
So I know, right in here,
I'd have a 3X.
Let me go ahead
and write that plus.

(Describer) ...in the first parentheses.

Now I need to divide
4X by X.
So 4X divided by X,
or like a 1X.
4 divided by 1,
that's just 4.
X to the 1st
divided by X to the 1st,
subtracting those exponents,
that's X to the 0,
and anything to the 0 power
is just 1.
This is really just like
4 times 1, which is just 4.
That means the second group--
or the second spot--
would have a 4.

(Describer) 3x plus 4.

We do the same process
with that 6X plus 8.
Okay, let's get this work
out of our way.
We need to find
the greatest common factor
between 6X and 8.
So we have a 6X,
we have an 8.
So as far as the 6
is concerned,
I know 1 times 6
would work,
and so would 2 times 3.
Then I have a factor of X.
As far as my 8 is concerned,
I know 1 times 8
would work,
and so would 2 times 4.
In this case, my greatest
common factor is 2.
Greatest common factor is 2.
Ooh--slid that down
by accident.
So what I would write here now
is plus 2,
because that's the greatest
common factor
for the second group,
right here.
Open up my parentheses.
Go ahead and throw
that plus sign in there.
Now I'll divide
each of these terms
by the greatest common factor.
I'm ignoring this work
over here for a minute.
So 6X divided by 2.
6 divided by 2,
that's 3.
I have an X up top
but nothing on the bottom,
so it's just carried along.
So I've got 3X
for the first term.
Now I need to divide 8 by 2.
Well, 8 divided by 2,
that's 4.
Then you see
in your second spot
that you have a 4,
then you look.
You have the same binomial
in your parentheses.
So that itself
is like a common factor
of this trinomial you were
trying to factor to start with.
To write your final answer,
this is what you do.
You have that X and this 2
that are
the greatest common factors.
When you factor those groups,
you bring them together.
You'd have X plus 2
as one factor.
Then that 3X plus 4
that's common to both.
That's another factor.
And you are all done.
You have factored
that trinomial
that had a leading coefficient
that was not 1.
There's a lot to these types
of problems.
We definitely have to do a few
so you can get
the hang of it.
Let's try another one.
Now I'm factoring 3X squared
plus 7X plus 2.
You remember the first step.
You multiply
the A and the C.
In this case,
the 3 and the 2.
So 3 times 2...
I know that's 6.
Now I need factors of 6
that are going to combine
to give me 7, okay?
So I start listing:
1 times 6; 2 times 3.
I need a positive 7.
So 1 and 6, that's 7.
You got it,
it's that first pair.
This is the point where
we split that middle term,
so I'll rewrite
this trinomial
as 3X squared plus X...
plus 6X plus 2.
I'm splitting that 7X
into 1X plus 6X.
It doesn't change
the meaning at all;
it just helps factor this
trinomial a little better.
Now that I've split
the middle term,
I'm at the point now
where I need to factor
these two groups,
these two pairs of binomials.
I'm going to get this work
out of our way.
Let's consider...
this first group
and then the second group.
Let's see how we're doing
with finding greatest
common factors here.
Between these two terms,
the greatest common factor.
The coefficient
of this one's 3
and of this one is 1.
As far as my numbers
are concerned,
the greatest number they have
in common as a factor is 1.
Now I see I have X squared
and I have X,
so if this term has 2X's
and this term has 1X,
they both have
at least 1X in common.
So the greatest common factor
of these 2 terms
is just 1X.

(Describer) She writes X.

I'm going to open up
the parentheses.
And now it's time to divide
each of these terms by X.
We'll come off over here.
So 3X squared
divided by X,
which is like a 1X, really,
to the 1st because
we don't see that exponent.
So 3 divided by 1, that's 3.
X squared divided
by X to the 1st,
that's just X because
we subtract our exponents here.
For my first term in here,
I know I have a 3X;
it'll be plus,
so get that in there.
For the second term,
I need to divide X by X.
Well, X divided by X,
that's just 1.
That means I have a 1 in here,
for that second group
of parentheses,
or that second term
in the parentheses.
It's time to do the same thing
with 6X plus 2.
Let me get this work
out of our way.

(Describer) So far, the answer is x times 3x plus 1.

All righty.
I need the greatest common
factor between 6X and 2.
I see that that's just a 2;
it's a constant term.
They won't
have any X's in common.
I need to focus
on these numbers here.
As far as 6 goes and 2 goes--
2 is prime,
so the only factors for 2
are 1 and 2.
And 2 is also a factor of 6,
so between these two terms,
my greatest common factor
is going to be 2.
So I'll write plus 2.
Go ahead and open
my parentheses.
I know I'm going to have
a plus sign in between.
Now it's time to divide
each of these terms
by our greatest common factor,
over here.
So 6X divided by 2.
So 6 divided by 2,
that's 3.
This X is just hanging along
for the ride, so 3X.
Then I have 2 divided by 2...
which is 1.
So then you look.
Here you notice
you have the same group
in those parentheses,
so we're at the point
of rewriting this.
Here we have our X plus 2,
which is out front.
We bring that together,
so X plus 2.
And then that factor
that was repeated:
3X plus 1.
And you are all done.
You factored that trinomial.
There are
a few steps to it,
but do it a few times
and you get the hang of it.
Let's try some more.
Factor completely:
2X squared plus 5X plus 3.
Again, we need to start out
by multiplying
2 times 3.
6 just keeps
popping up here.
So 2 times 3 is 6.
So factors of 6:
1 and 6...
2 and 3.
Now we need
the factors of 6
that are going to combine
to give us 5.
Let's see what we got here.
1 and 6, that's 7.
2 and 3, that is 5.
So I'll split
this middle term
and rewrite this
as 2X squared
plus 2X plus 3X plus 3.
Okay?
Do you remember
what we do next?
We're at the point
where we take
this first group,
we take the second group,
and factor each group.
We pull out the greatest
common factor in each group.
Let's get this work
out of the way.
So 2X squared and 2X.
They both
have that 2 in common.
The first term has X squared,
so there's a product
of two X's with that one.
The second term is 2X--
one X for that one.
For the numbers, 2 was
the greatest common factor.
For the variables, X was
the greatest common factor.
So my greatest
common factor: 2X.
Open up my parentheses.
I know I have a plus
in between.
Now I'm going to divide
each of these terms
by that
greatest common factor.
So 2X squared
divided by 2X.
So 2 divided by 2, that's 1.
X squared divided by X
to the 1st, that's X,
so basically it's X.
When I divide over there,
I get X.
Then I have 2X
divided by 2X.
Well, anything divided
by itself is 1,
so we know that 2X
divided by 2X is 1.
We've handled that first set.
Let's go on to the next group,
this 3X plus 3.
Let me get this work
out of the way.
All righty.
So 3X and a 3.
They both have 3--
there's a 3 involved
in each term.
For my number, the greatest
common factor is 3.
The first term has an X,
the second term doesn't,
so they don't have
an X in common.
They only have
a 3 in common.
I'll write my greatest
common factor, 3,
for this group,
open up my parentheses,
go ahead and put
the plus inside,
and start dividing.
So 3X divided by 3.
Well, 3 divided by 3,
I know that's 1.
X on top and no X
on the bottom,
so that carries along
for the ride.
I have, basically, 1X,
or just X.
Now, 3 divided by 3...
that's 1,
so you got a 1.

(Describer) 2x times, open parentheses, x plus 1, close parentheses, plus 3 times, open parentheses, x plus 1, close parentheses.

(female narrator)
2X times open parentheses,
X plus 1,
close parentheses,
plus 3 times,
open parentheses,
X plus 1,
close parentheses.
All right,
remember what we do next?
We're at the point now
to clean it up
and write our final answer.
We've got the 2X out here,
the 3 out front here.
In one set of parentheses
you'd have 2X plus 3.

(Describer) The first factor in the answer.

Then you'd have that factor
that was in both of those--
the repeated one,
that X plus 1.

(Describer) The other factor.

And you are all done,
you've factored completely.
Okay?
Let's try another.

(female narrator)
4X squared minus X minus 3.

(Describer) 4x-squared minus x minus 3.

Okay, so this one's
involving some negatives.
That'll be
a little different.
Other than that, the process
is exactly the same.
Start out by multiplying
A and C.
So 4 times 3, that's 12.
And I know I need
factors of 12
that will combine
to give me negative 1.
Once I list these factors,
they'll have different signs:
One number must be positive
and the other negative,
if when I combine them,
I get negative 1.
Let's list the factors:
1 and 12; 2 and 6;
3 and 4, right?
Now we have to find which one
of these pairs of numbers
will work and which
should be negative.
We know we're trying
to get negative 1,
so throw the first pair out.
There's no way
to combine a 1 and a 12
and get negative 1,
no matter which were negative.
Negative 1 plus 12
would be 11.
1 plus negative 12
would be negative 11.
So there's no way
it's the first pair.
2 and 6?
If the 2 were negative,
it'd be negative 2 plus 6,
and that's 4.
If the 6 were negative,
then it'd be a negative 4.
So that's not it;
it has to be this last pair.
I need to find which number
needs the negative.
Negative 3 plus 4
would be positive 1.
And I needed a negative 1,
so that means it's the 4
that's negative.
3 plus negative 4
will give me negative 1.
Now I'm ready to go ahead
and split my middle term.
I'm going to rewrite it as--
I've got my 4X squared--
I'm going
to write plus 3X
minus 4X minus 3, okay?
Do you remember
what comes next?
Go ahead,
you take your groups...
and you start
factoring the pairs, okay?
Let's get some more room
to work up here.
If I look
at these first terms,
the 4X squared
and the 3X.
4 and 3 have
nothing in common but 1,
but I do see I have
an X squared and an X.
These terms each
have an X as a factor.
So I'm going to write X
as the greatest common factor,
okay?
Let's get the parentheses up,
and get the plus sign
in there.
So 4X squared divided by X--
I'm ready to start
dividing these terms
by my greatest common factor.
That's essentially a 1X
to the 1st over there.
So 4 divided by 1.
That's 4X squared
divided by X,
that's just X.
So now I have 4X
over here.
And then 3X divided by X.
So 3X to the 1st
divided by 1X to the 1st.
So 3 divided by 1,
that's just 3.
X to the 1st
divided by X to the 1st
is X to the 0 power,
which is just 1.
Basically, 3 times 1,
that's not changing anything,
so I'll just leave it as 3.
Bring it over here.
Now I'm at the point
to go ahead
and look at these factors.
I have a negative 4X
and a negative 3.
The only thing
these two terms
have in common
is a negative 1, that's it.
Both of these terms
are negative.
We knew 3 and 4
had no factors in common.
And this is the only term
that has the X.
The only thing they have
in common is a negative 1.
Now it's time
to go through.
Just go ahead
and get that in there.

(Describer) The second set of parentheses.

And let's get this work
out of the way.
Here we go.
Now, I'm not going to write
the sign in here just yet
because I want to show you
something over here.
Now, I have negative 4X
divided by negative 1.
So negative 4X
divided by negative 1.
Negative 4 divided
by negative 1 is just 4.
X on top,
but no X on the bottom,
so it carries along
for the ride.
So I get 4X over here.
Then I have a negative 3
divided by negative 1.
So negative 3 divided by
negative 1,
that's positive 3.
So plus 3, okay?

(Describer) It's another 4x plus 3.

Remember what comes next?
You're at the finish line,
just about.
It's time to just write
that final answer.
So I see I have
the X out front here
and the negative 1
out front here.
So X minus 1.

(Describer) The first factor.

And both of these
have the 4X plus 3.
So 4X plus 3,
and you're all done.

(Describer) The second factor.

Exactly like we saw
when we were
factoring trinomials
where the leading
coefficient was 1,
check your answer by
multiplying your factors out.
At the last step,
you write your factors.
To check your answer,
multiply your factors together.
Use FOIL
and multiply them together
to get the starting problem.
You can still check
your answers that way.

(Describer) Next, 2x-squared plus x minus 15.

Okay? Let's continue.
Got one more here.
So you remember
the first step?
Good.
Multiply A and C together.
So 2 times 15--because
I'm going to ignore the sign
for a second--is 30.
So I'm going to factor 30.
So 1 times 30;
2 times 15;
3 times 10;
and 5 times 6--
and that's it for 30.
I need the factors
that will combine
to give me a positive 1.
And remember,
if you consider the sign now,
this was really a positive 2
times a negative 30.
So that means that--
write the negative
because now we're
considering the signs--
if the product
is negative,
then I had
to multiply together
a positive
with a negative number.
We need to check
which pair is going to work,
where one number is positive
and one is negative,
and the answer's 1
for that middle term.
We know there's no way
to combine 1 and 30
and the answer be positive 1;
there's no way.
If the 1 were negative,
it'd be 29.
And If the 30 were negative,
it'd be negative 29.
So that's not it.
2 and 15--
if the 2 were negative,
the answer would be 13.
If the 15 were negative,
the answer is negative 13.
So that's not it.
3 and 10--if the 3
were negative, it'd be 7.
If the 10 were negative,
it'd be negative 7, so nope.
We know it has to be this pair,
but which one's negative?
If the 5's negative--
negative 5 plus 6--
that is positive 1.
That's the pair
that we want:
negative 5
and positive 6.
Let's split our middle term.
We're going to rewrite
this as 2X squared
minus 5X plus 6X...
minus 15, okay?
We didn't change
the meaning at all;
we're just rewriting
that 1X
as negative 5X plus 6X.
Let's get this work
out of the way
because now it is time
to take these two groups
and start looking at these
separately
to get the greatest
common factors.
If I consider
2X squared and 5X--
2 and 5 are both
prime numbers,
so the only factor
they have in common is 1.
As far as the variable part
goes, X squared and an X,
they both have at least
one factor of X.
So the greatest common factor
between these two terms
is X.
Go ahead and open up
my parentheses.
I'll start dividing here.
And I'm going to
write my "minus" in this time.
So 2X squared
divided by X.
2X squared divided by X.
There's a 1 and 1
I don't see.
So this will end up being:
2 divided by 1 is 2,
X squared divided by X is X.
So 2X for the first term.
And now I have--I've already
written my negative
over here, but to show you
why I did,
because I'm dividing
negative 5 by X.
I knew the answer
would be negative,
dividing a negative
and a positive.
Go ahead and put
the invisible 1's in.
Negative 5 divided by 1
is negative 5.
And X divided by X is 1.
So basically,
my answer's negative 5.
And I already wrote
the negative part.
I'll drop the 5 in there.

(Describer) X times 2x minus 5.

Repeat the same process
with that second group.
Get that out of the way.
Okay, so 6X and 15.
You may need to write
the factors down for this one.
It may not be clear
what it is at first.
For 6, you have 1 and 6;
2 and 3.
You have an X in there,
so there's a factor of X.
And for 15:
1 and 15; 3 and 5.
And now you can look and see.
15 has no X, so there's
no factor of X in that one.
My greatest common factor
here is 3.
I'll come back to my problem.
I'll put my 3 in there.
I'll put the minus sign
in there this time
because I know,
like I did over here,
I knew the answer
would be a negative.
Let's start dividing.
Let's get some more room.
So 6X divided by 3.
That's 2X.
6 divided by 3 is 2.
I have an X up top
but nothing on the bottom,
so it carries along.
Then I have negative 15
divided by 3...
which is negative 5.
And I already wrote
the negative part in there.
I knew it was going to be
negative, so there's my 5.
You remember what's next?
You're ready
to write that final answer.
Look and see which terms
were out front.
You've got the X and the 3.
So X plus 3.
Then in my parentheses I have
2X minus 5, and 2X minus 5.
That means that's
that second factor here:
2X minus 5.
And you are all done.
So that initial trinomial
that we started with
factors to X plus 3
times 2X minus 5, okay?
You're ready to try
a couple of these.
Go ahead and take some time,
remember those steps,
and work your way
through these.
Check your answer
before you press play.
Press pause
and see how you do.
To compare with me,
press play.

(Describer) Title: Factor completely.
Number One: 5x-squared plus 11x plus 2.
Number Two: 3x-squared minus 13x plus 4.

(female narrator)
Factor completely.
Number 1:
5X squared plus 11X plus 2.
Number 2:
3X squared minus 13X plus 4.
You ready to check?
Let's see.
When I factored
that first trinomial,
I got 5X plus 1,
and X plus 2.
And when I factored
the second one,
I got 3X minus 1,
and X minus 4.
This is how I did it.

(Describer) She goes to the first problem by itself.

First thing, remember,
we're following our steps.
We multiply
the A and the C.
So 5 times 2, that's 10.
Now I need factors of 10.
I need to find
the pair of factors that,
when I combine them, I get 11.
As far as 10 goes, I know
1 times 10 will give me 10.
So will 2 times 5.
I need the pair
that gives me 11.
You probably spotted that
pretty quickly--the 1 and 10.
1 plus 10 is 11.
You know that's the pair
of factors you want.
Now jump back
to your trinomial,
and you can split
that middle term.
So 5X squared plus X
plus 10X plus 2.
Now you're ready
to take it in groups,
and find the greatest common
factor in each group.
As far as 5X squared
and 5 goes,
the only factor
they have in common is X.

(Describer) She writes x and the first parenthesis.

If I go ahead and do my
division, like I need to...
So 5X squared divided by X...
which is basically
a 1X to the first, right?
5 divided by 1, that's 5.
X squared divided by X
to the 1st, that's X.
I knew I had 5X right here.
Let's close that off,
put my plus sign in there.
Now I need X divided by X.
Well, anything divided
by itself is 1.
That's how I knew the second
term in there was 1.
So let's get that work
out of the way.
Do that second group.
Okay.
So between 10X and 2.
2's prime,
so the only factors
are 1 and itself--
1 and 2.
It doesn't have an X,
so the greatest common factor
between 10X and 2 is 2.
I'll write my plus 2,
open up my parentheses.
I have a plus sign in between.
I'm ready to divide
to see what actually goes
in this group of parentheses.
So 10X divided by 2.
10 divided by 2 is 5,
X on top but nothing
on the bottom...
Moving the screen.
Let's get that crazy mark
out of the way.
There we go.
Okay, so 10X divided by 2.
10 divided by 2 is 5.
X up top but nothing
on the bottom,
so we're just
carrying that along.
So in my group,
first term is 5X.
Now I need to divide 2 by 2.
So 2 divided by 2,
that's 1.
And you got your 5X plus 1.
You probably noticed
in these problems,
if you don't have the
same thing in the parentheses,
go back and check
because something went wrong.
These kinds of problems
should end up
with that same group
inside your parentheses.
Okay? That's a hint
while you're working.
Now you're at the point,
just bring everything together.
You've got your X
and you've got that 2 out front.
So X plus 2.
And then I have
my 5X plus 1.
And you're all done.
If you wrote these
in another order,
like "5X plus 1" first
and "X plus 2" second--
that's fine.
You can multiply
in any order you want,
according to
the commutative property.
If your factors
are reversed from mine,
you're still right.
Here's how I got
that last one.
Same process,
multiply the A and C.
So 3 times 4, that's 12.
So I need my factors
for 12.
So 1 and 12;
2 and 6; 3 and 4.
I ignore the signs
to start with--
when everything's positive,
you can ignore the signs
because they'll be positive.
It's when there's a negative
in there that you want to go,
"Something else
is going to happen."
Ignore them to start,
but then consider
that it's negative as you
work through the problem.
I'm there now,
where I must consider
this middle term's negative.
If I'm multiplying
to get a positive number,
because I know
that's positive--
even though it's the 4,
and to work through
the problem, it's 12,
it's still positive;
that sign is the same.
And the middle term
is negative.
So the only way I can multiply
two numbers together
and get something positive,
but combine them
and get something negative,
is if the numbers themselves
are both negative.
I must consider that these
are negative numbers,
and then I need to find the pair
that will give me negative 13.
Negative 1 plus negative 12
is negative 13.
What do you know?
It was the first one.
So that's the pair we need.
Now we we can
go back to our problem
and split that middle term.
So 3X squared minus X
minus 12X plus 4, okay?
I'm going to get that old work
out of the way
because more is coming.
All right, you remember
what we do now?
Break it up
into those groups.
So I've got 3X squared
minus X.
So between these two terms,
your greatest common factor
is just X.
So divide each
of these terms by X.
So 3X squared divided by X,
which is basically
a 1X to the 1st, right?
So 3 divided by 1,
that's 3.
X squared divided by X is X.
So over here,
I've got my 3X.
I won't write the minus yet;
I'll bring it
over here with me
and put it
with my answer.
I'm dividing negative X
by positive X.
Basically,
a negative 1X to the 1st
divided by a positive 1X
to the 1st.
Negative 1 divided
by positive 1 is negative 1.
X to the 1st divided by
X to the 1st.
That's X to the 0,
which is really 1,
which doesn't change anything.
If I multiply negative 1
times 1, it's still negative 1.
So I'll leave that
and bring it over here.
Got my minus 1.
Now I'm at the point where
I can handle the second group.
So let's get this old work
out of the way.
Now I see I have a negative 12X
and a positive 4.
I need to find out what's
the greatest common factor
between these two terms?
Because this is negative,
I'm going to go ahead
and pull that out front.
I'm going to pull
a negative common factor
out of each of these--
this is what I mean.
As far as 12 goes,
I've got 1 and 12;
2 and 6; 3 and 4.
As far as 4 goes,
I've got 1--
keep sliding that down--
as far as 4 goes,
I've got 1 and 4;
2 and 2.
So the greatest common factor
between these numbers is 4.
But I could say
that it's negative 4, okay?
Because if I treat this
like it's a negative 12,
which basically it is,
then I can say,
I already know 4
is my common factor.
I'll jump down to and 3 and 4
and say, that's the same
as 3 times negative 4,
which is negative 12.
And negative 1 times negative 4
is also positive 4.
So I'll pull out
a negative 4 over here
for my greatest common factor.
A little math magic.
Now I'll bring these here
and now it's time to divide.

(Describer) ...parentheses.

I need to divide each of
those terms by that negative 4.
Let's get this work
out of the way.
So I have negative 12X
divided by negative 4...
which--ooh, 12X.
So negative 12 divided
by negative 4, that's 3.
X up top but nothing
on the bottom,
so it just carries along.
You see you've got your 3X.
Then I have positive 4
divided by negative 4.
Positive 4 divided
by negative 4 is negative 1.
You see we have
our minus 1.
Now we're at the last step,
to go ahead and write
the final answer.
So I'll bring these together
in a group of parentheses.
I'd have X minus 4.
Then for my second set,
3X minus 1,
that factor
that was in both of those.
Remember, you can always
multiply these factors together
to check your answer
and get that trinomial
that we started with.
I hope you're feeling confident
about factoring trinomials
where you leading
coefficient is not 1,
and that knowing
how to factor trinomials
where your leading
coefficient is 1
helped you through
this lesson.
Hope to see you
back here soon. Bye!

(Describer) Accessibility provided by the US Department of Education.