# How do you use the factor theorem to determine whether x+3 is a factor of -4x^3 + 5x^2 + 8?

You evaluate this polynomial at $x = - 3$.
Let $P \left(X\right) = - 4 {X}^{3} + 5 {X}^{2} + 8$. If $X + 3$ is a factor of $P$, then $P \left(- 3\right) = 0$. Let's evaluate $P$ at $3$.
$P \left(- 3\right) = - 4 \cdot {\left(- 3\right)}^{3} + 5 \cdot {3}^{2} + 8 = 108 + 45 + 8 \ne 0$ so $X + 3$ is not a factor of $P$.