Find the remainder when the polynomial function $f(x) = x^3 + 4x + 15$ is divided by $x + 2$ using the Remainder Theorem. Write the divisor $x + 2$ in the form $x - c$ to get $x - (-2)$, meaning $c = -2$. According to the Remainder Theorem, the remainder is equal to $f(c)$. Evaluate the function at $c = -2$: $f(-2) = (-2)^3 + 4(-2) + 15$. Simplifying this expression gives $-8 - 8 + 15$, which equals $-1$. The remainder is $-1$.