For what value of k is the polynomial p(x)

(d) −3

Let:

$p(x)=2 x^{3}-k x^{2}+3 x+10$

Now,

$x+2=0 \Rightarrow x=-2$

$p(x)$ is completely divisible by $(x+2)$.

$\therefore p(-2)=0$

$\Rightarrow 2 \times(-2)^{3}-k \times(-2)^{2}+3 \times(-2)+10=0$

$\Rightarrow-16-4 k-6+10=0$

$\Rightarrow-12-4 k=0$

$\Rightarrow 4 k=-12$

$\Rightarrow k=\frac{-12}{4}$

$\Rightarrow k=-3$