Question

Check whether $(x-2)$ is a factor of $x^3-2x^2-5x+4$.

Answer 1

To check that $x-2$ is the factor of $x^3-2x^2-5x+4$:

The value of $x-2=0$ $⟹$ $x=2$.

So, put $x=2$ in expression, we get,

$f\left(x\right)=x^3-2x^2-5x+4$

$f\left(2\right)=(2{)}^3-2(2{)}^2-5\left(2\right)+4$

$\Rightarrow f\left(2\right)=8-2\times 4-5\times 2+4$

$\Rightarrow f\left(2\right)=8-8-10+4$

$\Rightarrow f\left(2\right)=-6$.

Remainder is not $0$, when $x-2$ divides the polynomial $x^3-2x^2-5x+4$.

Thus $x-2$ is not a factor of polynomial $x^3-2x^2-5x+4$.