Question

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$p\left(x\right)=2x^3-9x^2+x+15,g\left(x\right)=2x-3$

Answer 1

$p\left(x\right)=2x^3-9x^2+x+15g\left(x\right)=2x-3$

By remainder theorem, when p(x) is divided by ( 2x − 3), then the remainder = $p\left(\frac{3}{2}\right)$.

Putting x = 3 in p(x), we get

$p\left(\frac{3}{2}\right)=2(\frac{3}{2}{)}^3-9(\frac{3}{2}{)}^2+\left(\frac{3}{2}\right)+15=\frac{27}{4}-\frac{81}{4}+\frac{3}{2}+15=\frac{-54}{4}+\frac{6}{4}+\frac{60}{4}=\frac{-54+6+60}{4}=\frac{12}{4}=3$

∴ Remainder = 3

Thus, the remainder when p(x) is divided by g(x) is 3.