Question

Find the remainder using remainder theorem, when:

$4x^3-12x^2+11x-5$ is divided by $2x-1$

Answer 1

According to remainder theorem, when $f\left(x\right)$ is divided by $(2x-1)$, Remainder $=f\left(\frac{1}{2}\right)$

$f\left(x\right)=4x^3-12x^2+11x-5$

$f\left(\frac{1}{2}\right)=4(\frac{1}{2}{)}^3-12(\frac{1}{2}{)}^2+11\left(\frac{1}{2}\right)-5$

$=4\times \frac{1}{8}-12\times \frac{1}{4}+11\times \frac{1}{2}-5$

$=\frac{1}{2}-3+\frac{11}{2}-5$

$=\frac{12}{2}-8$

$=6-8=-2$

$\therefore$ Remainder =$=-2$