Question

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

Answer 1

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

$\dfrac{3x^4+2x^3-x^2-x-6}{x^2+1}=3x^2+2x-4+\dfrac{-3x-2}{x^2+1}$

so that the remainder is $-3x-2$.