How do you solve #(x^{4}-2x^{3}-30x^{2}+x+6)\div (x^{2}+5x+2)#?

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Answer 1 · 2017-01-20T16:16:09

The answer is #=x^2-7x+3#

Let's do the long division

#color(white)(aaaa)##x^4-2x^3-30x^2+x+6##color(white)(aaaa)##∣##x^2+5x+2#

#color(white)(aaaa)##x^4+5x^3+2x^2##color(white)(aaaaaaaaaaaa)##∣##x^2-7x+3#

#color(white)(aaaaa)##0-7x^3-32x^2+x#

#color(white)(aaaaaaa)##-7x^3-35x^2-14x#

#color(white)(aaaaaaaaa)##-0+3x^2+15x+6#

#color(white)(aaaaaaaaaaaaa)##+3x^2+15x+6#

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

Therefore,

#(x^4-2x^3-30x^2+x+6)/(x^2+5x+2)=x^2-7x+3#