Question

Use synthetic division and the remainder theorem to determine $f\left(0.2\right)$ given that
$f\left(x\right)=0.1x^3-0.6x^2-0.6$

Answer 1

From remainder theorem, $f\left(0.2\right)=$ remainder of $\frac{f\left(x\right)}{x-0.2}$

To determine remainder, use synthetic division.

$$\begin{array}{cc}\begin{array}{c}\\ 0.2\\ \end{array}& \begin{array}{cccc}0.1& -0.6& 0& -0.6\\ & 0.02& -0.116& -0.0232\\ 0.1& -0.58& -0.116& -0.6232\end{array}\end{array}$$

$\Rightarrow f\left(0.2\right)=-0.6232$