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Question

Divide 3t4+5t37t2+2t+2 by t2+3t+1 and find quotient and remainder.

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Solution

Lets divide 3t4+5t37t2+2t+2 by t2+3t+1,

3t24t+2t2+3t+1 )¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 3t4+5t37t2+2t+2 3t4±9t3±3t2––––––––––––––– 4t310t2+2t4t312t24t––––––––––––––––– 2t2+6t+22t2±6t±2–––––––––––– 00

So the quotient, q(x) = 3t^2 - 4t + 2 and the remainder, r(x) = 0

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