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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Updated on: 10-Oct-2022

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