How do you find the quotient and remainder when #(3x^3-2x^2+x+7)# is divided by #(x^2-2x+5)#?

1 Answer
Narad T.
Nov 6, 2016

The remainder is #=-6x-13#
The quotient is #=3x+4#

Explanation:

Let's do the long division
#color(white)(aaaa)##3x^3-2x^2+x+7##color(white)(aaa)##∣##x^2-2x+5#
#color(white)(aaaa)##3x^3-6x^2+15x##color(white)(aaaaa)##∣##3x+4#
#color(white)(aaaaaa)##0+4x^2-14x+7#
#color(white)(aaaaaaaa)##+4x^2-8x+20#
#color(white)(aaaaaaaaaa)##+0-6x-13#

The remainder is #=-6x-13#
The quotient is #=3x+4#

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