Question

What is the remainder when $f\left(x\right)=-3x^{17}+x^9-x^5+2x$is divided by$x+1$?

Short answer

The remainder is $1$.

Step-by-step solution

Step 1. Concept used 

The Remainder Theorem states that if f is a polynomial function and $f\left(x\right)$is divided by $x-c$, then the remainder is $f\left(c\right)$.

Step 2. Use the Remainder Theorem 

Using the remainder theorem when the function $f\left(x\right)=-3x^{17}+x^9-x^5+2x$is divided by $x+1$then the remainder is given as $f(-1)$.

Now the function value is evaluated as

$$\begin{gathered} f(-1)=-3{(-1)}^{17}+{(-1)}^9-{(-1)}^5+2(-1) \\ f(-1)=3-1+1-2 \\ f(-1)=1 \end{gathered}$$

So the remainder is$1$.