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Review for MA098 Factoring If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. 1) 15x2 + 26x + 8 1) Solve the problem. 2) The area of a circle is 100 square meters. Find its radius. Factor. 3) 64x2 + 48xy + 9y2 3) 4) x2 + 10xy + 25y2 4) Factor out the largest possible common factor. 5) 21y3 - 6y2 + 15y Solve. 5) 6) x2 + 5x - 14 = 0 6) Solve the equation. 7) 5x2 - 40x + 75 = 0 Factor. 2) 7) 8) 100 - x2 y2 8) Solve the equation. 9) x2 + 4x - 60 = 0 9) Factor by grouping. 10) 12x2 + 7xt - 12t2 10) If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. 11) 16x2 - 81 11) Solve the equation. 12) 13d2 - 7d = 0 Solve the problem. 13) The equation D = 12) 1 n(n-3) gives the number of diagonals, D, for a polygon with n sides. 2 Find the number of sides n for a polygon that has 27 diagonals. 1 13) Factor as completely as possible. If unfactorable, indicate that the polynomial is prime. 14) x2 - x - 35 14) If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. 15) 72a 4 - 98b2 15) Factor by grouping. 16) 15x2 + 19x + 6 16) Factor. 17) z 2 - 2z + 1 17) Find a polynomial in factored form for the shaded region. 18) 18) 13 15 Factor out the largest possible common factor. 19) 6m 9 - 9m 7 - 18m 5 19) Factor using the trial and error method. 20) 20x2 + 7x - 6 20) Factor. 21) 49x2 - 9 21) 22) 64x2 + 144xy + 81y2 22) Factor out the largest possible common factor. 23) 32x7 y9 - 24x2 y6 + 36x4 y4 23) Factor as completely as possible. If unfactorable, indicate that the polynomial is prime. 24) x4 - 3x2 - 4 24) Solve the equation. x2 + 13x = -11 25) 2 25) 2 Factor. 26) 6x2 - 6x - 36 26) If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. 27) 24xy - 20by + 18x - 15b 27) Factor. 28) 81x2 + 144xy + 64y2 28) If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. 29) 36x + 12x2 - 12xy 29) Factor by grouping. 30) 10z 2 + 11z - 6 30) Solve the problem. 31) The width of a rectangle is 6 kilometers less than twice its length. If its area is 80 square kilometers, find the dimensions of the rectangle. 31) Factor. 32) s18 - t16 32) Factor by grouping. 33) 9x - 108 + xy - 12y 33) Solve the problem. 34) The force in newtons needed to stretch a certain spring x centimeters from its resting position is given by the polynomial function f(x) = 8x2 where 8 is the spring constant. Find the force needed to stretch the spring 3 centimeters. 35) The sum of two numbers is 10, and the sum of their squares is 52. Find the numbers. 34) 35) If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. 36) 4k3 m + 28k2 m 2 + 49km3 36) Factor by grouping. 37) 12x2 + 10x - 18x - 15 37) Factor. 38) x2 - x - 30 38) Factor as completely as possible. If unfactorable, indicate that the polynomial is prime. 39) x3 + 3x2 - 25x - 75 3 39) If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. 40) 8x2 - 28x - 16 40) Factor using the trial and error method. 41) 10x2 + 19x + 6 41) Factor by grouping. 42) xy + 7x - 4y - 28 42) If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. 43) x4 - 256 43) Factor out the largest possible common factor. 44) w(z - 12) - 8(z - 12) 44) Solve the equation. 45) x2 + 9x - 64 = 3(x - 8) 45) Factor. 46) x7 - 10x6 + 9x5 46) Factor as completely as possible. If unfactorable, indicate that the polynomial is prime. 47) x4 + 2x3 + 125x + 250 47) Factor. 48) x2 + 15x + 54 48) Factor by grouping. 49) 7x2 - 5x - 2 49) If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. 50) 21x2 - 91x - 70 50) 4 Answer Key Testname: FACTORING 1) (3x + 4)(5x + 2) 2) 10 m 3) (8x + 3y)2 4) (x + 5y)2 5) 3y(7y2 - 2y + 5) 6) x = -7, x = 2 7) x = 3, 5 8) (10 - xy)(10 + xy) 9) x = -10, 6 10) (3x + 4t)(4x - 3t) 11) (4x + 9)(4x - 9) 7 ,0 12) d = 13 13) 9 sides 14) Prime 15) 2(6a 2 + 7b)(6a 2 - 7b) 16) (3x + 2)(5x + 3) 17) (z - 1)2 18) (13 - x)(15 + x) 19) 3m 5 (2m 4 - 3m 2 - 6) 20) (4x + 3)(5x - 2) 21) (7x + 3)(7x - 3) 22) (8x + 9y)2 23) 4x2 y4 (8x5 y5 - 6y2 + 9x2 ) 24) (x + 2)(x - 2)(x2 + 1) 25) x = -11, -2 26) 6(x + 2)(x - 3) 27) (4y + 3)(6x - 5b) 28) (9x + 8y)2 29) 12x(3 + x - y) 30) (2z + 3)(5z - 2) 31) length = 8 km, width = 10 km 32) (s9 + t8 )(s9 - t8 ) 33) (x - 12)(9 + y) 34) 72 newtons 35) 4 and 6 36) km(2k + 7m)2 37) (2x - 3)(6x + 5) 38) (x + 5)(x - 6) 39) (x + 5)(x - 5)(x + 3) 40) 4(2x + 1)(x - 4) 41) (2x + 3)(5x + 2) 42) (y + 7)(x - 4) 43) (x2 + 16)(x + 4)(x - 4) 44) (z - 12)(w - 8) 45) x = -10, 4 46) x5 (x - 9)(x - 1) 5 Answer Key Testname: FACTORING 47) (x + 2)(x + 5)(x2 - 5x + 25) 48) (x + 6)(x + 9) 49) (7x + 2)(x - 1) 50) 7(3x + 2)(x - 5) 6