Question

State whether the following statement is true or false.

$(x-1)$ is a factor of $x^3-27x^2+8x$.

• A. True
• B. False

Answer 1

The correct option is B False

Let $p\left(x\right)=x^3-27x^2+8x$

$g\left(x\right)=x-1$

$p\left(1\right)={\left(1\right)}^3-27{\left(1\right)}^2+8\left(1\right)$

$=1-27+8$

$=9-27$

$=-18\ne 0$

so by factor theorem $x-1$ is not a factor of $p\left(x\right)$