Factoring Using the Distributive Property

Section 10.8

Warm UpFactor completely: 100x² - 121

(10x – 11)(10x + 11)

Homework Check / Questions

Factoring Out the GCFNOTE: We have done this already, but now

we are doing it right awayThe first step of factoring is always

checking to see if you can factor out the GCF. If you can: then do it and factor what left

inside the parenthesis.If you cannot: then go ahead and factor

in the ways we already have!

Example: Factor .1. Factor out GCF

(What’s multipliedinto every term?)

2. Factor what’s leftin parenthesis

45: 1, 3, 5, 9, 15, 4520: 1, 2, 4, 5, 10, 20

5 𝑥2(9𝑥2−4)

9 𝑥2−45 𝑥2(3𝑥+2)(3 𝑥−2)

(3 𝑥+2)(3 𝑥−2)

You Try! Factor: 27w³ - 3w.

3w(3w+1)(3w-1)

Too Easy? Factor: 5x³ - 25x² - 30x.

5x(x – 6)(x + 1)

You’re Bored? Factor: 75x – 3x².

-3x(x – 25)

Factoring by GroupingWe’ve already done this within a different

context.

We are distributing backwards!

𝑎 (𝑏+𝑐 )+𝑑 (𝑒+ 𝑓 )=(𝑎+𝑑)(𝑒+ 𝑓 )

Example: Factor .1. Put parenthesis around

first two and last two terms. (Put a “+” in between.)

2. Factor out GCF from each pair.

3. Reverse distribute.

4. Factor anything that still needs to be factored.

𝑥2 (𝑥+2 )+9(𝑥+2)

(𝑥2+9)(𝑥+2)

(𝑥¿¿3+2𝑥2)+(9 𝑥+18)¿

(𝑥+3)(𝑥−3)(𝑥+2)

When do I factor by grouping?

When there are 4 terms!

Your turn! Factor x³ - 2x² - 9x + 18.

(x + 3)(x – 3)(x – 2)

Keep ‘em comin’. Factor x³ + 2x² - 36x - 72

(x + 6)(x – 6)(x + 21)

Round Table Activity!We will get into small groupsEach person will get a worksheetAfter a set amount of time, everyone must rotate

papersYou must pick up from where the previous person left

off on the paper. You cannot go back and fix problems that have already been finished. If the person was in the middle of a problem, you can edit

that specific problemAt the end, your group can discuss the problems to

see if there needs to be any changesAt the end, you will staple your group’s pages

together

Homework: pg. 632 #14-24 even