How do you divide #( -x^3+ 2x^2+9x-5 )/(x - 5 )#?

1 Answer
Ratnaker Mehta
Jun 14, 2016

Clearly, quotient =# -(x^2+3x+6),# and, remainder = #-35#.

Explanation:

Numerator #=-x^3+color(red)2x^2+color(blue)9xcolor(green)(-5)= -x^3+color(red)5x^2color(red)(-3)x^2+color(blue)15xcolor(blue)(-6)xcolor(green)(+30-35)=-x^2(x-5)-3x(x-5)-6(x-5)-35=(x-5)(-x^2-3x-6)-35.#

Hence, the given rational function #={(x-5)(-x^2-3x-6)-35}/(x-5)={-(x-5)(x^2+3x+6)/((x-5))}-(35}/(x-5).#

Clearly, quotient =# -(x^2+3x+6),# and, remainder = #-35#.

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