Question

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$\left(px\right)=6x^3+13x^2+3,g\left(x\right)=3x+2$

Answer 1

$p\left(x\right)=6x^3+13x^2+3g\left(x\right)=3x+2$

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

Putting x = $\frac{-3}{2}$ in p(x), we get

$p\left(\frac{-3}{2}\right)=6(\frac{-3}{2}{)}^3+13(\frac{-3}{2}{)}^2+3=\frac{-16}{9}+\frac{52}{9}+3=\frac{-16}{9}+\frac{52}{9}+\frac{27}{9}=\frac{-16+52+27}{9}=\frac{63}{9}=7$

∴ Remainder = 7

Thus, the remainder when p(x) is divided by g(x) is 7.