How do you use long division to divide #(x^4+5x^3+6x^2-x-2)div(x+2)#?

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Answer 1 · 2017-01-28T06:45:28

The answer is #=color(blue)(x^3+3x^2-1)#

Let's do the long division

#color(white)(aaaa)##x^4+5x^3+6x^2-x-2##color(white)(aaaa)##||##color(red)(x+2)#

#color(white)(aaaa)##x^4+2x^3##color(white)(aaaaaaaaaaaaaaaa)##||##color(blue)(x^3+3x^2-1)#

#color(white)(aaaaa)##0+3x^3+6x^2#

#color(white)(aaaaaaa)##+3x^3+6x^2#

#color(white)(aaaaaaaaaa)##+0+0-x-2#

#color(white)(aaaaaaaaaaaaaaaaa)##-x-2#

#color(white)(aaaaaaaaaaaaaaaaa)##-0-0#

The quotient is #=color(blue)(x^3+3x^2-1)#