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Name: ____________________________
Mr. Art
Date: _____________
Period: ___________
Review # ______
Factoring
Part I: Mixed Review
Directions: Use your knowledge of factoring to answer the following questions below.
1. Expressed in factored form, the binomial 2x2y – 4xy3 is equivalent to:
(1) 2xy(x -2y)
(2) 2xy(xy – 4y)
(3) 2xy(x – 2y2)
(4) 2x2y3(y-2)
2. What is the GCF of 9xy – 54x2y3?
(1) 9
(2) xy
(3) 9xy
(4) 6xy
3. One of the factors of x2 – 64 is:
(1) (x + 4)
(2) (x – 8)
(3) 2x
(4) (2x – 8)
4. A common factor of x2 + 7x +10 and x2 – 25 is:
(1) x -5
(2) x +5
(3) x + 2
(4) x2
5. One of the factors of 25x2 – 9 is 5x – 3. Find the other factor.
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Part II: Greatest Common Factor (GCF)
Directions: Factor each of the following using the GCF Method
Review:
Step 1: Pull out the GCF and open parentheses
Step 2: Divide each term of the expression by the GCF and put in parentheses
6. 3x3 – 6x2
7. 24a2b + 18abc
Part III: Difference of Two Perfect Squares (DOTS)
Directions: Factor each of the following expressions using the DOTS Method.
Review:
Step 1: Open two sets of parentheses (one with a +, one with a - )
Step 2: Take the square root of each term and place them inside parentheses
8. x2 – 81
9. 4x2 – 25y2
10. 169 – k6
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Part IV: Factoring Trinomials using the Product & Sum (P&S) Method
ax2 + bx + c
Review
Step 1: Find two numbers that add to “b” and multiply to “c”
Step 2: Place them in the parentheses in the blanks (x ___)
with + for positive numbers and – for negative numbers
Directions: Factor each of the following trinomials.
11. y2 + y - 20
12. 20 + 9x + x2
Part V: Factoring Completely
Review:
1. First look for a GCF. Factor using the GCF method, if possible.
2. Look inside the parentheses
 Check for Difference of Two Perfect Squares (DOTS)
OR
 Factor the trinomial
Directions: Factor each of the following expressions completely.
13. 3x2 + 15x + 12
14.
81x4 – 16y4
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Part VI: Dividing a Polynomial by a Binomial
Steps
1. Factor both the numerator and denominator completely.
2. Reduce any like terms.
15.
2x  2
x 1
18. (d2 + 4d – 32) ÷ (d - 4)
16.
x 2  16
x4
17.
19.
3x  18
2 x  12
20.
x 2  14 x  45
x 9
x2  x  6
3x 9
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Part VII: Factoring Mixed Review
Directions: Factor each of the following expressions. Where necessary, factor the
expressions completely.
21. 4y2 - 196
22. 2ax – 5x
23. 5x2 - 45
24. 4x2 – 24x - 28
25. 49m2 – 100n2
26. x2 – x - 56
27. x4 - 1
28. 6x2 – 6y2
29. 2x3 – 8x
30. 5x2 + 20x + 20
31. 5x3 - 10x2 - 15x
32. x2 + 3x - 4
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