How do you find the quotient of (x^3+6x^2-x-30) divided by (x^2+8x+15)?

2 Answers
Cem Sentin
Jun 6, 2018

Quotient is #x-2#

Explanation:

#x^3+6x^2-x-30#

=#x^3+8x^2+15x-2x^2-16x-30#

=#x*(x^2+8x+15)-2*(x^2+8x+15)#

=#(x^2+8x+15)*(x-2)#

Hence quotient is #x-2#

Alan P.
Jun 6, 2018

#(x^3-6x^2-x-30)div(x^2+8x+15)=color(blue)(x-2)#

Explanation:

It is possible to solve this by factoring but factoring cubic equations can be time consuming.
As an alternative, I would suggest using simple polynomial long division.

#color(white)("XXXXXXXXX")ul(color(white)("xx")xcolor(white)("x")-2color(white)("xxxxxxxxxxxxx"))#
#x^2+8x+15" ) "x^3color(white)("x")+6x^2color(white)("x")-xcolor(white)("x")-30#
#color(white)("XXXXXXXXXx")ul(x^3color(white)("x")+8x^2+15x)#
#color(white)("XXXXXXXXXxxxx")-2x^x-16xcolor(white)("x")-30#
#color(white)("XXXXXXXXXxxxx")ul(-2x^x-16xcolor(white)("x")-30)#

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