Question

By using the remainder theorem, divide the polynomial $x^3-2x^2-4x-1$ by $x-1$ and find the remainder.

Answer 1

Given, $p\left(x\right)=x^3-2x^2-4x-1$ is divided by $x-1$.

By Remainder Theorem, we know,

if $p\left(x\right)=x^3-2x^2-4x-1$ is divided by $x-1$, then the remainder obtained is $p\left(1\right)$.

That is,

$p\left(1\right)=(1{)}^3-2(1{)}^2-4\left(1\right)-1$

$=1-2-4-1$

$=-6$.

Hence, the required remainder is $-6$.