ALGEBRA – LESSON 69Factoring Trinomials

Be ready to grade the homework!

When you multiply two binomials, you can remember the results given by the distributive property by means

of the FOIL method.

(3x + 4)(x + 5)

= 3x 2 + 19x + 20

Product of First Terms

Product of Outer Terms

Product of Inner Terms

Product of Last Terms

Multiply the First, Outer, Inner, and Last terms.

Don’t forget to add like terms.

= 3x2 + 15x + 4x + 20

*This is not in your notes. Just watch.

2

Let’s Review

(x + 3)(x – 5)

= x 2 – 2x – 15

– 5x + 3x – 15

Product of First Terms

Product of Outer Terms

Product of Inner Terms

Product of Last Terms

Multiply the First, Outer, Inner, and Last terms.

Don’t forget to add like terms.

= x2

Let’s Review

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.

1. List the factors of the constant term.

When we take an equation and break it down into smaller parts that will multiply to get the original equation, we have

the equation.factored

2. Select the factors that will ADD up to the middle coefficient.

Which one is the “constant term”?y2 + 14y + 45

Note: the original equation MUST be written in descending order first!!

Factor (just watch)

x2 + 10x + 16What are the factors of 16?

1 , 16 -1 , -16 2 , 8 -2 , -8 -4 , -4 4 , 4

Which of these add up to 10?

(x )(x )

Plug in the factors that you chose including their signs.

+ 2 + 8

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

x2 + 5x - 24What 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?

(x )(x )

Plug in the factors that you chose including their signs.

- 3 + 8

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

x2 – 10x + 16What are the factors of 16?

Which of these add up to -10?

(x )(x )

Plug in the factors that you chose including their signs.

– 2 – 8

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

1 , 16 -1 , -16 2 , 8 -2 , -8 4 , 4 -4 , -4

Factor

14y + y2 + 45What are the factors of 45?

Which of these add up to 14?

(y )(y )

You must rewrite this in descending order FIRST!

+ 5 + 9

Check your work with FOIL.

y2 + 9y + 5y + 45

y2 + 14y + 45

#3

1 , 45 -1 , -45 3 , 15 -3 , -15 5 , 9 -5 , -9

y2 + 14y + 45

Factor

-6n + n2 + 8What are the factors of 8?

Which of these add up to -6?

(n )(n )

You must rewrite this in descending order FIRST!

– 2 – 4

Check your work with FOIL.

n2 – 4n – 2n + 8

n2 – 6n + 8

#4

1 , 8 -1 , -8 2 , 4 -2 , -4

n2 – 6n + 8

Homework: PS 69