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If $x+2$ is a factor of $x^2+ax+8$, then find the value of $a$.
Given: $x+2$ is a factor of $x^2+ax+8$.
To do: To find the value of $a$.
Solution:
As given, $x+2$ is a factor of $x^2+ax+8$
Let $x+2=0$
$\Rightarrow x=-2$, put this value in the polynomial $x^2+ax+8$
$\Rightarrow ( -2)^2+a( -2)+8=0$
$\Rightarrow 4-2a+8=0$
$\Rightarrow -2a+12=0$
$\Rightarrow 2a=12$
$\Rightarrow a=\frac{12}{2}$
$\Rightarrow a=6$
Thus, $a=6$.
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