## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$1$
The Remainder theorem states that the remainder of a function $f(x)$ after dividing by $(x-r)$ is $f(r)$. As per the given equation, when $f(x)=-3x^{17}+x^9-x^5+2x$ is divided by $x+1$, then by the remainder theorem $f(-1)$ represents the remainder of the function. We simplify the given equation as follows: $f(-1)=-3(-1)^{17}+(-1)^9-(-1)^5+2(-1) \\=3-1+1-2 \\=1$