How do you simplify #\frac { x ^ { 3} + 15x ^ { 2} - 4x - 6} { x + 3}#?

1 Answer
Barney V.
Sep 14, 2017

#x^2+12x-40# and remainder of #114/(x+3)#

Explanation:

#(x^3+15x^2-4x-6)/(x+3)#

by long division:-

#color(white)(..........)color(white)(.)color(magenta)(x^2+12x-40#
#x+3|overline(x^3+15x^2-4x-6)#
#color(white)(...........)ul(x^3+3x^2)#
#color(white)(....................)2x^2-4x#
#color(white)(...................)ul(12x^2+36x)#
#color(white)(..................................)-40x-6#
#color(white)(...................................)ul(-40x-120)#
#color(white)(.................................................)114#

#color(magenta)((x^3+15x^2-4x-6) / (x+3) = x^2+12x-40# and remainder#color(magenta)(114/((x+3))#

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