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What is the reminder if f(x)=3x^4+2x^3-x^2-x-6 divide by x^2+1

What is the reminder if f(x)=3x^4+2x^3-x^2-x-6 divide by x^2+1-example-1

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Attached is a walkthrough of the long division algorithm. The final line gives the remainder term. Basically, this translates to


(3x^4+2x^3-x^2-x-6)/(x^2+1)=3x^2+2x-4+(-3x-2)/(x^2+1)

so that the remainder is
-3x-2.
What is the reminder if f(x)=3x^4+2x^3-x^2-x-6 divide by x^2+1-example-1
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