Question

Which of the following is the factor of the polynomial
$x^3-3x^2-10x+12$ ?

• A. $x-0$
• B. $x-1$
• C. $x-2$
• D. $x+1$

Answer 1

The correct option is B

$x-1$

Factor theorem:
" If p(a) =0, then $x-a$ is the factor of $p\left(x\right)$ "

Let $p\left(x\right)=x^3-3x^2-10x+12$

Consider $x-1$ which is in the form of $x-a$.

so, $a=1$ .

So, $p\left(a\right)=a^3-3a^2-10a+12$

$\Rightarrow$ $p\left(1\right)=1^3-3(1{)}^2-10(1)+12$

$\Rightarrow$ $p\left(1\right)=1-3\left(1\right)-10\left(1\right)+12$

$\Rightarrow$ $p\left(1\right)=1-3-10+12=0$

So, $x-1$ is the factor .