Question

Find the remainder when $p\left(x\right)=x^3-6x^2+14x-3$ is divisible by $g\left(x\right)=1-2x$ and verify the result by long division

Answer 1

Given : $p\left(x\right)=x^3-6x^2+14x-3,g\left(x\right)=1-2x$

$p\left(\frac{1}{2}\right)=(\frac{1}{2}{)}^2-6(\frac{1}{2}{)}^2+14\left(\frac{1}{2}\right)-3$

$=\frac{1}{8}-\frac{6}{4}+7-3$

$=\frac{1-12+32}{8}$

$=\frac{21}{8}$

This can be verified by the actual division too.