How do you divide (2x^3-4x^2+16x-8) / (x-2)?

1 Answer
Jim G.
Apr 8, 2018

2x^2+16+24/(x-2)

Explanation:

"one way is to use the divisor as a factor in the numerator"

"consider the numerator"

color(red)(2x^2)(x-2)cancel(color(magenta)(+4x^2))cancel(-4x^2)+16x-8

=color(red)(2x^2)(x-2)color(red)(+16)(x-2)color(magenta)(+32)-8

=color(red)(2x^2)(x-2)color(red)(+16)(x-2)+24

"quotient "=color(red)(2x^2+16)," remainder "=24

rArr(2x^3-4x^2+16x-8)/(x-2)=2x^2+16x+24/(x-2)

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