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Name
Date
Mr. Megdanis/Ms. Cranwell
Test Date Friday 11-13-10
Study Guide for Factor By Grouping Test
Factor By Any Technique
Examples:
(x2 -7 x + 12)
(x - _ ) (x - _ )
(x - 3 ) (x - 4)
(x2 + x - 12)
(x + _ ) (x - _ )
(x + 4 ) (x - 3)
If the last number is + you know that both signs will be the same
The sign of the middle term is what sign you will use.
Create a T-Chart if needed to find the factors of the last number that add up to the middle
number.
If the last number is - you know that both signs will be different.
One sign will be negative, one sign will be positive.
Create a T-Chart if needed find the factors of the last number that add up to the middle
number.
1. w2 – w – 30
(w-6)(w+5)
2. n2 + 4n – 12
(n+6)(n-2)
3. x2 – 11xy + 10y2
(x-10y)(x-y)
4. c2 + 16c + 48
(c+12) (c+4)
Factor By Grouping
Example:
4 (x – 2) – 3x (x – 2)
GCF: (x – 2)
( x – 2) (4 – 3x)
5. 3t (t2 – 9) + 12 (t2 - 9)
(t+3) (t+3) 3 (t +4)
3(t+3)(t+3)(t+4)
6. c (4 – 2c) – 6 (4 – 2c)
(4-2c) (c-6)
2(2-c)(c-6)
7. a2 (a -5) + (a – 5)
(a-5) (a2 +1)
8. 7k (k + 8) -2 (k +8)
(k+8) (7k -2)
Are both sets of parenthesis the same?
Factor out the Greatest Common Factor
Once you factor that out, put the remaining factors into parenthesis next to it.
Factor By Grouping
Example:
2ab + 6ac + 3b + 9c
2ab + 6ac
+ 3b + 9c
GCF: 2a
GCF: 3
2a (b + 3c)
3 (b + 3c)
GCF: ( b + 3c)
(b + 3c) (2a + 3)
9. x3 + x2 -6x -6
x2(x+1)-6(x+1)
(x+1) (x2-6)
10. b3 + 4b2 + 3b + 12
(b+4) (b2+3)
11. p3 – 2p2 + 4p -8
p2(p-2)+4(p-2)
(p2+4) (p-2)
12. rs + 5r + st + 5t
(s+5) (r+t)
Count the terms, are there 4?
If there are 4 terms, separate them into TWO pairs.
Factor the GCF from each pairs.
Factor out the GCF of both pairs.
Next to the GCF write what remains in parenthesis
Factor By Grouping
Example:
(x2 -7 x + 12)
x2 -3x - 4x + 12
x2 -3x -4x + 12
GCF: x GCF: -4
x(x-3) -4(x - 3)
GCF: (x - 3)
(x - 3) ( x – 4)
13. a2 + 3a – 10
(a +5) (a-2)
14. k2 + 5k – 24
(k+8)(k-3)
15. x2 – 9x – 36
(x-12)(x+3)
16. d2 + 34d – 35
(d+35)(d-1)
-3 • -4 = 12 Last number
Find what multiplies together to equal the last term
-3 + -4 = -7 Middle number
Find what adds together to equal the middle term
Then replace those numbers for the middle term with an “x” attached
Count the terms, if there are 4 terms separate the problem into TWO pairs.
Factor the GCF from each pairs.
Factor out the GCF of both pairs.
Next to the GCF write what remains in parenthesis.
17. b2 – 5b – 6
(b-6)(b+1)
18. c2 –c – 30
(c-6)(c+5)