SOLUTION: Find the quotient and remainder using synthetic or long division x^5-3x^3+5x^2-12/x+2

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Question 1056896: Find the quotient and remainder using synthetic or long division
x^5-3x^3+5x^2-12/x+2
Answer by math_helper(2461) About Me  (Show Source):
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%28x%5E5-3x%5E3%2B5x%5E2-12%29%2F%28x%2B2%29
= x%5E4+ +%28-2x%5E4-3x%5E3%2B5x%5E2-12%29%2F%28x%2B2%29
= x%5E4+-+2x%5E3 + %28x%5E3%2B5x%5E2-12%29%2F%28x%2B2%29
= x%5E4+-+2x%5E3+%2B+x%5E2 + %283x%5E2-12%29%2F%28x%2B2%29
= x%5E4+-+2x%5E3+%2B+x%5E2+%2B+3x + %28-6x-12%29%2F%28x%2B2%29
= x%5E4+-+2x%5E3+%2B+x%5E2+%2B+3x+-+6 (with no remainder)