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MTH 098 TEST 3 SUMMER 2010 NAME____________________________________________ Each problem counts 3 points. THE TEST COUNTS 120 POINTS. SHOW WORK EXCEPT FOR FACTORING PROBLEMS! DO NOT USE DECIMALS! Graph the linear equation. Show at least THREE POINTS. 1) x = y + 4 y 5 -5 5 x -5 Find the square. 2) ( 5 a - 3 )2 Simplify by writing the expression with positive exponents. Do not use decimals. 2a -6 b5 3) 12a -10 b8 Factor out the greatest common factor. 4) 42x9 y8 + 42x7 y5 + 54x2 y2 Factor completely. Use a negative common factor. 5) -30x3 - 10x Factor by grouping. 6) r3 + r2 + 2r + 2 Factor as completely as possible. Factor out a negative if the first term is negative. 7) 15z 2 + 2z - 8 8) -5x2 + 21xy - 4y2 Factor completely. Write ʺprimeʺ if it is not factorable. 9) 72a 4 - 98b2 10) 4x2 + 49 11) x4 - 16 Factor. 12) 25x2 + 60xy + 36y2 Solve the equation. Show your factoring. Express your answer as a solution set. 13) x(x - 5) = 24 14) 6b2 + 13b - 2 = -8 15) 20r2 = 4r Find all values that make the expression undefined. x2 - 36 16) x2 - 11x + 18 17) 4q - 6 q2 + 4 Find the numerical value of the expression for the given value. 8 x2 + 7 x , x = -3 18) 3x Write the rational expression in lowest terms. a 2 - 25 19) a 2 + 9a + 20 Write the expression in lowest terms. 2k - 4 20) 8 - 4k Multiply. Write the answer in lowest terms. 2t2 - 3t - 9 3t2 + 13t - 30 · 21) t2 + 3t - 18 3t2 - 2t - 5 Divide. Write the answer in lowest terms. z 2 + 4z z 2 + 12z + 32 ÷ 22) z 2 + 15z + 56 z 2 + 9z + 14 Perform the indicated operation. Write the answer in lowest terms. x2 - 7x x + 2 x2 - 5x - 14 · ÷ 23) x + 7 7x x2 - 14x + 49 Perform the indicated operation and express in lowest terms. 3x + 16 x + 8 24) - x2 - 2x - 24 x2 - 2x - 24 Perform the indicated operation and write the answer in lowest terms. 6 2 25) + x + 4 x 26) x 4 8 + - x - 2 x + 2 x2 - 4 Add or subtract. Write the answer in lowest terms. 2 5 27) + 6 x - 9 9 - 6 x Find the square root. 144 28) - 49 29) - 289 Find the root. 5 30) -243 Simplify the radical. Assume that all variables represent nonnegative real numbers. 31) 25y8 100m 9 n 12 32) Simplify. 33) 3 128z 17 Simplify and add or subtract wherever possible. 34) 9 19 - 19 35) -5 6 + 8 150 Simplify the expression. 36) 6 3 ( 11 + 3 ) 37) (8 7 + 3 2)(10 7 + 7 2) Simplify. 38) (5 - 3 5)2 Find the product. Assume all variables have non -negative values. 39) ( 6 + 3 )( 6 - 3 ) Write the quotient in lowest terms. 54 - 18 200 40) 12 Answer Key Testname: MTH 098 TEST 3 SU 10 1) y 10 5 -10 -5 -5 -10 2) 25 a 2 - 30 a + 9 a4 3) 6b3 4) 6x2 y2 (7x7 y6 + 7x5 y3 + 9) 5) -10x(3x2 + 1) 10) Prime 11) (x2 + 4)(x + 2)(x - 2) 12) (5x + 6y) 2 13) {-3, 8} 3 2 14) - , - 2 3 15) 0, 1 5 16) 9, 2 17) Never undefined 17 18) - 3 19) a - 5 a + 4 20) - 1 2 21) (2t + 3) (t + 1) 22) z + 2 z 23) x + 7 7 24) 2 x - 6 25) 8x + 8 x(x + 4) x + 8 x + 2 27) -3 6 x - 9 28) - 5 6) (r2 + 2)(r + 1) 7) (3z - 2)(5z + 4) 8) -(5x - y)(x - 4y) 9) 2(6a 2 + 7b)(6a 2 - 7b) 26) 10 x 12 7 29) Not a real number 30) -3 31) 5y4 32) 10m 4 n 6 m 3 33) 4z 5 2z 2 34) 8 19 35) 35 6 36) 6 33 + 18 37) 602 + 86 14 38) 70 - 30 5 39) 3 9 - 30 2 40) 2