ALGEBRA – LESSON 69
Factoring Trinomials
Be ready to grade the homework!
Let’s Review
When you multiply two binomials, you can remember
the results given by the distributive property by means
of the FOIL method.
Multiply the First, Outer, Inner, and Last terms.
Product of
First Terms
(3x + 4)(x + 5)
= 3x2
Product of
Outer Terms
+ 15x
Product of
Inner Terms
+ 4x
Product of
Last Terms
+ 20
= 3x 2 + 19x + 20
Don’t
forget to
add like
terms.
*This is not in your notes. Just watch.
2
Let’s Review
Multiply the First, Outer, Inner, and Last terms.
Product of
First Terms
(x + 3)(x – 5)
= x2
Product of
Outer Terms
– 5x
Product of
Inner Terms
+ 3x
= x 2 – 2x – 15
Product of
Last Terms
– 15
Don’t
forget
to add
like
terms.
We have learned how to multiply binomials using the FOIL
method. Now we will learn how to factor them. I usually call
this “Un-foiling” just to help you remember the process.
When we take an equation and break it down into smaller parts
that will multiply to get the original equation, we have
factored the equation.
1. List the factors of the constant term.
Which one is the “constant term”?
y2 + 14y + 45
2. Select the factors that will ADD up to the middle coefficient.
Note: the original equation MUST be written in descending
order first!!
Factor (just watch)
What are the
factors of 16?
1 , 16
-1 , -16
2, 8
-2 , -8
-4 , -4
4, 4
Which of these
add up to 10?
x2 + 10x + 16
(x + 2)(x + 8)
Plug in the factors that you chose
including their signs.
It doesn’t matter which order you
place the factors into the equation.
(x + 8)(x + 2)
Check your work with FOIL.
x2 + 2x + 8x + 16
x2 + 10x + 16
Factor
What are the
factors of -24?
1, -24
-1 , 24
2 , -12
-2 , 12
6 , -4
-6 , 4
3 , -8
-3 , 8
Which of these
add up to 5?
x2 + 5x - 24
(x - 3 )(x + 8)
Plug in the factors that you chose
including their signs.
It doesn’t matter which order you
place the factors into the equation.
(x + 8)(x – 3)
Check your work with FOIL.
x2 – 3x + 8x – 24
x2
+ 5x – 24
#1
Factor
What are the
factors of 16?
1 , 16
-1 , -16
2, 8
-2 , -8
4, 4
-4 , -4
Which of these
add up to -10?
x2 – 10x + 16
(x – 2)(x – 8 )
Plug in the factors that you chose
including their signs.
It doesn’t matter which order you
place the factors into the equation.
(x – 8)(x – 2)
Check your work with FOIL.
x2 – 2x – 8x + 16
x2
– 10x + 16
#2
Factor
What are the
factors of 45?
1 , 45
-1 , -45
3 , 15
-3 , -15
5, 9
-5 , -9
Which of these
add up to 14?
14y + y2 + 45
You must rewrite this in descending
order FIRST!
y2 + 14y + 45
(y + 5 )(y + 9 )
Check your work with FOIL.
y2 + 9y + 5y + 45
y2 + 14y + 45
#3
Factor
What are the
factors of 8?
1, 8
-1 , -8
2, 4
-2 , -4
Which of these
add up to -6?
-6n + n2 + 8
You must rewrite this in descending
order FIRST!
n2 – 6n + 8
(n – 2 )(n – 4 )
Check your work with FOIL.
n2 – 4n – 2n + 8
n2 – 6n + 8
#4
Homework: PS 69