Find the value of a, if x + 2 is a factor of

We have to find the value of a if $(x+2)$ is a factor of $\left(4 x^{4}+2 x^{3}-3 x^{2}+8 x+5 a\right)$.

$S$ ubstituting $\mathrm{x}=-2$ in $4 \mathrm{x}^{4}+2 \mathrm{x}^{3}-3 \mathrm{x}^{2}+8 \mathrm{x}+5 \mathrm{a}$, we get :

$4(-2)^{4}+2(-2)^{3}-3(-2)^{2}+8(-2)+5 \mathrm{a}=0$

or, $64-16-12-16+5 \mathrm{a}=0$

or, $5 \mathrm{a}=-20$

or, $\mathrm{a}=-4$

$\therefore$ If $(x+2)$ is a factor of $\left(4 x^{4}+2 x^{3}-3 x^{2}+8 x+5 a\right), a=-4$