How do you solve #(x^4-9x^3-7x^2-8x+2)/(x^2+x+1)#?

1 Answer
George C.
Feb 25, 2018

#(x^4-9x^3-7x^2-8x+2)/(x^2+x+1) = x^2-10x+2#

Explanation:

We can long divide the coefficients like this:
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finding that:

#(x^4-9x^3-7x^2-8x+2)/(x^2+x+1) = x^2-10x+2#

Alternatively, note that:

#(x^2+x+1)(x-1) = x^3-1#

So:

#(x^4-9x^3-7x^2-8x+2)/(x^2+x+1) = ((x^4-9x^3-7x^2-8x+2)(x-1))/(x^3-1)#

#color(white)((x^4-9x^3-7x^2-8x+2)/(x^2+x+1)) = (x^5-10x^4+2x^3-x^2+10x-2)/(x^3-1)#

#color(white)((x^4-9x^3-7x^2-8x+2)/(x^2+x+1)) = (x^3(x^2-10x+2)-1(x^2-10x+2))/(x^3-1)#

#color(white)((x^4-9x^3-7x^2-8x+2)/(x^2+x+1)) = (color(red)(cancel(color(black)((x^3-1))))(x^2-10x+2))/color(red)(cancel(color(black)((x^3-1))))#

#color(white)((x^4-9x^3-7x^2-8x+2)/(x^2+x+1)) = x^2-10x+2#

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