Final answer:
f(-4) equals zero for the given polynomial implies that -4 is a root, meaning (x + 4) is a factor of the polynomial.
Step-by-step explanation:
When f(-4) for the polynomial function f(x) = x³ + 11x² + 34x + 24 equals zero, it indicates that -4 is a root of the polynomial, meaning that if you substitute -4 into the polynomial for x, the resulting value is zero. This implies that (x + 4) is a factor of the polynomial equation. To determine the other factors or roots of this cubic polynomial, you could perform polynomial division to divide the polynomial by (x + 4) and then use the quadratic formula on the resulting quadratic equation to find the remaining roots.