Question

What is the remainder when $f\left(x\right)=2x^{20}-8x^{10}+x-2$is divided by$x-1$?

Short answer

The remainder is $-7$.

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 $f\left(x\right)=2x^{20}-8x^{10}+x-2$is divided by $x-1$then the remainder is given as $f\left(1\right)$.

Now the function value is evaluated as

$$\begin{gathered} f\left(1\right)=2{\left(1\right)}^{20}-8{\left(1\right)}^{10}+1-2 \\ f\left(1\right)=2-8+1-2 \\ f\left(1\right)=-7 \end{gathered}$$

So the remainder is$-7$.