Question

Divide p(x)=x^4+6x^3+7x^2-6x-8 by x+4. What is the remainder

Answer 1

Use the remainder theorem; dividing a polynomial $p(x)$ by $x-c$ leaves a remainder equal to $p(c)$. Here

$p(x)=x^4+6x^3+7x^2-6x-8$

$\implies p(c)=(-4)^4+6(-4)^3+7(-4)^2-6(-4)-8=\boxed{0}$