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

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

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

Putting x = -2 in p(x), we get

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

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