Question

Use synthetic division and the remainder theorem to determine $f(-2)$ given that $f\left(x\right)=5x^4-4x^3-x^2+5$

Answer 1

From remainder theorem, $f(-2)=$ remainder of $\frac{f\left(x\right)}{x+2}$

To determine remainder, use synthetic division.

So, let's divide $f\left(x\right)$ by $-2$ and we have

$$\begin{array}{cc}\begin{array}{c}\\ -2\\ \end{array}& \begin{array}{ccccc}5& -4& -1& 0& 5\\ & -10& 28& -54& 108\\ 5& -14& 27& -54& 113\end{array}\end{array}$$

$\Rightarrow f(-2)=113$