State True or False:

Is $(x-3)$ a factor of $3x^2-7x-6$?

The correct option is B. True

According to Factor Theorem,
if $(x-a)$ is a factor of a polynomial, say $p\left(x\right)$
then $p\left(a\right)=0$

Now, if $(x-3)$ is a factor of $p\left(x\right)=3x^2-7x-6$, then $p\left(3\right)$ should be $0$.

$\Rightarrow p\left(3\right)=3(3{)}^2-7\times 3-6$

$=27-21-6$

$=0$

$\Rightarrow p\left(3\right)=0$

Hence, $(x-3)$ is a factor of $3x^2-7x-6$.