Question

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

• A. (x - 2)(x + 3)(x - 4)
• B. (x + 2)(x + 3)(x + 4)
• C. (x + 2)(x - 3)(x - 4)
• D. (x - 2)(x - 3)(x - 4)

Answer 1

The correct option is A

(x - 2)(x + 3)(x - 4)

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 .