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Name: ___________________________________ Date: ________________ 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 = _____________________ 1 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 p2 22) x 2 7 x 10 x 2 2 x 15 23) 2y2 9y 4 4y2 4y 3 2 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. 3