How do you long divide # (x^4+10x^3+8x^2-59x+40) div (x^2+3x-5)#?

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Answer 1 · 2017-02-28T10:15:52

The remainder is #=0# and the quotient is #=(x^2+7x-8)#

Let's perform the long division

#color(white)(aaaa)##x^4+10x^3+8x^2-59x+40##color(white)(aaaa)##|##x^2+3x-5#

#color(white)(aaaa)##x^4+3x^3-5x^2##color(white)(aaaaaaaaaaaaaaa)##|##x^2+7x-8#

#color(white)(aaaaa)##0+7x^3+13x^2-59x#

#color(white)(aaaaaaa)##+7x^3+21x^2-35x#

#color(white)(aaaaaaaaa)##+0-8x^2-24x+40#

#color(white)(aaaaaaaaaaaaa)##-8x^2-24x+40#

#color(white)(aaaaaaaaaaaaaaaa)##-0-0+0#

The remainder is #=0# and the quotient is #=(x^2+7x-8)#