How do you divide ( x^4-2x^3-2x^2+11x+12)/(2x-6)?

1 Answer
George C.
Jan 7, 2016

Long divide coefficients to find:

(x^4-2x^3-2x^2+11x+12)/(2x-6) = 1/2x^3+1/2x^2+1/2x+7

with remainder 27

Explanation:

I like to long divide coefficients, but first note that 2x-6 = 2(x-3), so to simplify the calculation, let's divide by x-3, then divide the result (and any remainder) by 2 at the end:

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We find:

(x^4-2x^3-2x^2+11x+12)/(x-3) = x^3+x^2+x+14

with remainder 54.

Hence (dividing by 2):

(x^4-2x^3-2x^2+11x+12)/(2x-6) = 1/2x^3+1/2x^2+1/2x+7

with remainder 27

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