# Is x-3 a factor of x^3-6x^2-x+30?

If $a$ is a root of a polynomial $P \left(x\right)$ (that is $P \left(a\right) = 0$), then $P \left(x\right)$ is divisible by $\left(x - a\right)$
So, we need to evaluate $P \left(3\right)$. That is:
${3}^{3} - \left(6 \cdot {3}^{2}\right) - 3 + 30 = 27 - 54 - 3 + 30 = 27 - 57 + 30 = 0$
and so the polynomial give is divisible by $\left(x - 3\right)$