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Quiz5solutions

# Quiz5solutions - MAC1105 Quiz#5 Solutions In the top-right...

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Unformatted text preview: MAC1105: Quiz #5 Solutions July 12, 2010 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. Factor: 2x2 - 6x - 36 = 2(x2 - 3x - 18) = 2(x - 6)(x + 3) 2. Factor: 4x2 + 4x - 15 AC method: Find factors of 4(-15) = -60 that add up to 4. After some eort, we arrive at 10 and -6. So: 4x2 + 4x - 15 = 4x2 + 10x - 6x - 15 = (4x2 + 10x) - (6x + 15) = 2x(2x + 5) - 3(2x + 5) = (2x - 3)(2x + 5) 3. State the formula for the dierence of cubes: a3 - b3 = (a - b)(a2 + ab + b2 ) 4. Multiply the following rational expressions (hint - factor and reduce rst): x - 1 x2 + x - 2 x2 - 4 x2 - 2x - 1 = (x + 2)(x - 1) x-1 2 (x + 2)(x - 2) x - 2x - 1 = = x-1 (x - 1) (x - 2) x2 - 2x - 1 (x - 1)2 , x = -2 (x - 2)(x2 - 2x - 1) 1 ...
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