# Find the value of a for which (x − 4) is a factor of

Question:

Find the value of $a$ for which $(x-4)$ is a factor of $\left(2 x^{3}-3 x^{2}-18 x+a\right)$.

Solution:

Let:

$f(x)=2 x^{3}-3 x^{2}-18 x+a$

$(x-4)$ is a factor of $f(x)=2 x^{3}-3 x^{2}-18 x+a$.

$\Rightarrow f(4)=0$

$\Rightarrow 2 \times 4^{3}-3 \times 4^{2}-18 \times 4+a=0$

$\Rightarrow 8+a=0$

$\Rightarrow a=-8$

Hence, the required value of a is -8.