Question

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$p\left(x\right)=2x^3+x^2-15x-12,g\left(x\right)=x+2$.

Answer 1

$p\left(x\right)=2x^3+x^2-15x-12$

​$g\left(x\right)=x+2$

By remainder theorem, when p(x) is divided by (x + 2), then the remainder = p(−2).

Putting x = −2 in p(x), we get

$p\left(-2\right)=2\times {\left(-2\right)}^3+{\left(-2\right)}^2-15\times \left(-2\right)-12=-16+4+30-12=6$

∴ Remainder = 6

Thus, the remainder when p(x) is divided by g(x) is 6.