Question

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$\left(px\right)=x^3-2x^2-8x-1,g\left(x\right)=x+1$

Answer 1

$p\left(x\right)=x^3-2x^2-8x-1g\left(x\right)=x+1$

By remainder theorem, when p(x) is divided by ( x+1), then the remainder = $p(-1)$.

Putting x = -1 in p(x), we get

$p(-1)=(-1{)}^3-2(-1{)}^2-8(-1)-1=-1-2+8-1=4$

∴ Remainder = 4

Thus, the remainder when p(x) is divided by g(x) is 4.