Name: ______________________________
Mr. Art
Date: ______________
Period: _____________
Factoring
Mixed Review
Part I: Factoring Completely
Factoring Completely – The process of factoring multiple times until a number or expression cannot be
further factored.
Review:
Step 1: First look for a GCF. Factor using the GCF method, if possible.
Step 2: Look inside the parentheses
 Check for the Difference of Two Perfect Squares (DOTS)
OR
 Factor the trinomial into the product of two binomials
Directions: Factor each of the following expressions completely.
1) 4x + 8y
2) 3x2 - 48
3) 2x3 – 50x
4) 2x3 – 2x2 – 12x
5) 3x2 – 18x + 24
6) x4 - 81
7) 6 x 2  30 x  36
8) y 5  4 y 4  3 y 3
9) 3 x 2  75
10) 7m 6  7m 2
11) y 2 
9
25
12) 5 x 3  55 x 2  120 x
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Part II: Greatest Common Factor (GCF)
Review:
Step 1: Pull out the GCF and open parentheses
Step 2: Divide each term of the expression by the GCF and place in parentheses
Directions: Factor each of the following using the Greatest Common Factor
13) 7x4 – 14xy
14) 3ab2 – 6a2b
15) 5x3 + 6xy
16) 12x7y – 4xy
17) 81r3s – 9
18) xyz + 3x2y2z2
Part III: Difference of Two Perfect Squares (DOTS)
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
Directions: Factor each of the following expressions using The Difference of Two Perfect Squares
19) x2 – 225
20) x4 – 49
21) 100 – x6
22) 16x2 - 25
23) 25x8 – 144y2
24) 4b2 – 169y2
25) x4 – y2
26) x2 + 49
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Part IV: Factoring Trinomials (Product & Sum or P&S)
Review:
ax2 + bx + c
Step 1: Find two numbers that multiply to “c” AND also add to “b”
Step 2: Place them in the parentheses in the blanks (x ___) (x___)
with + for positive numbers and – for negative numbers
Directions: Factor each of the following trinomials.
27) y2 + 6y + 5
28) x2 - 9x + 20
29) x2 + 7x + 12
30) m2 -2m - 15
31) x2 + 6x + 8
32) x2 + 9x -36
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