What is the remainder when
f(x) = -3x^17 + x^9 - x^5 + 2x is divided by x + 1?
The Factor/Root Theorem: Given the polynomial $\displaystyle P(x)$ then $\displaystyle \left( {x - a} \right)$ is factor of $\displaystyle P(x)$ if and only if $\displaystyle a$ is a root or $\displaystyle P(a)=0$. As a result of the theorem if $\displaystyle P(x)$ is divided by $\displaystyle \left( {x - b} \right)$ the remainder is $\displaystyle P(b)$.