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Algebra - Chapter 8 Review Worksheet
Directions: Write the prime factorization for each of the following monomials.
1) 4800c 3 d 2  __________________________
2)  50ab 2  _________________________
Directions: Find the GCF of each group of integers or monomials.
3) 44, 100
GCF = ___________
4) 12 x 2 , 32 x 2 yz, 18xy 2
GCF = ___________
Directions: Factor each of the following polynomials completely. You may use any strategy you choose.
If a polynomial cannot be factored, write “prime.”
5) 24m 2 n 2  4m 2 n  6n = _________________
6) 55 p 2  11 p 4  44 p 5 = _____________________
7) x 2  4 x  3 = ___________________
8) y 2  9 y  18 = _____________________
9) a 2  14a  24 = __________________
10) 3m 2  8m  3 = ______________________
11) 32  8 y 2 = __________________
12) 2 y 2  11y  18 = _____________________
13) x 4  81 = ______________________
14) 3x 3  x 2 y  3x  y = _____________________
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15) 16 y 2  8 y  1 = ___________________
16) 6t 3  14t 2  12t = _______________________
Directions: Solve the following equations by factoring.
17) 5 p  16 p 2  0
18) y 2  5 y  4  0
19) 3b 2  18b  10b  49
20) 25d 2  100  0
Directions: Simplify each of the following rational expressions. State the excluded values of the
variables.
21)
p 2  8 p  12
p2
22)
x 2  7 x  10
x 2  2 x  15
23)
2y2  9y  4
4y2  4y  3
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24) Madison is building a fenced, rectangular dog pen. The width of the pen will be 3 yards less than the
length.
a. Write an expression for the area of the dog pen.
b. If the area of the dog pen is 28 square yards, write and solve an algebraic equation to find
the measure of the length.
25) The width of a box is fifty inches more than the length, and the height of the box is 2 inches less
than the length. The volume of the box is 4800 cubic inches.
a. Label the dimensions of the box at the right
using algebraic expressions. (use l for length)
b. Write an equation to represent the volume of the box and solve it to find the length.
c. Find the height.
d. Find the width.
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