If $( x+1)$ is a factor of $x^2-3ax+3a-7$, then find the value of $a$.

Given: $( x+1)$ is a factor of $x^2-3ax+3a-7$.

To do: To find the value of $a$.

The given expression is

$x^2-3ax+3a-7$

If $( x+1)$ is a factor of $P( x)$, then the value of $P( x)=0$, at $x=-1$.

On putting $x=-1$ in given expression:

$P( -1)=( -1)^2-3a( -1)+3a-7$

$\Rightarrow 1+3a+3a-7=0$

$\Rightarrow 6a-6=0$

$\Rightarrow 6a=6$

$\Rightarrow a=\frac{6}{6}$

Therefore, the value of $a$ is $1$.