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
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