Aim #49: How do we factor polynomials completely?
Homework: Handout
Do Now: Factor each expression.
2
2
1. x - 49
2
4
2. x - 9x + 20
3
3. 4a b - 10a b
3
2
4. 2x - 3x - 14
4
22
6. xx ++x100
9
2
5. -6x + 13x - 6
Sometimes, one problem will require us to use more than one type of factoring and
we will have to factor multiple times.
We need to __________ ___________ and use all of the necessary methods.
*** ALWAYS see if we can factor out a _______ FIRST!!! ***
Factor Completely:
2
1) 8x + 20x + 8
2
3) wx - 16wx
4
3
2
2) 6x - 2x - 4x
2
2
4) 100x - 36y
Factor the following completely.
1) 2x2 - 18
2) 3x2 + 6x - 24
3) z8 - z4
4) 2ax2 - 2ax - 12a
5) z3 - z
6) 16x2 - x2y4
7) 4x2 - 6x - 4
8) -8x3 - 18x2 - 4x
9) ax2 - 3ax - 54a
10) 2x3 - 14x2 + 24x
11) -2x2 + 3x + 9
12) 9x2 + 18xy + 9y2
13) ax5 - a5x5
14) x2(x + 2) - 9(x + 2)
15) 3x2 + 12x + 12
16) 9a4 - 36b4
17) 5x2 - 25x + 30
18) 6a2 - 6a4
19) xy + 2x + 3y + 6
3
2
21) ax + 3ax - 64ax - 192a
4
2
20) x - 15x - 250
8
4
22) 3x - 47x - 16
Sum it up!!!
To factor completely, ALWAYS start by seeing if a GCF can be factored out.
Then determine if trinomial factoring or DOTS can be used. Factor until the
expression inside of the parentheses is prime.