Find the remainder when the polynomial function $f(x) = x^3 + 3x + 19$ is divided by $x + 2$ using the Remainder Theorem. First, express the divisor in the $x - c$ format. The divisor $x + 2$ can be written as $x - (-2)$, which gives $c = -2$. The Remainder Theorem states that the remainder is $f(c)$. Therefore, evaluate the function at $c = -2$: $f(-2) = (-2)^3 + 3(-2) + 19$. Simplifying gives $-8 - 6 + 19$, which equals $5$. The remainder is $5$.