# How do you use the factor theorem to determine whether x-3 is a factor of 2x^3-11x^2+12x+9?

$x - a$ is a factor of polynomial $P \left(x\right)$ if and only if $P \left(a\right) = 0$
$2 {\left(3\right)}^{3} - 11 {\left(3\right)}^{2} + 12 \left(3\right) + 9 = 54 - 99 + 36 + 9 = \left(54 + 36 + 9\right) - 99 = 99 - 99 = 0$
So $x - 3$ is a factor of $2 {x}^{3} - 11 {x}^{2} + 12 x + 9$