Final answer:
To find the zeros of f(x) = x^3 + 5x^2 - 41x - 45, we can substitute -9 for x in the equation and solve.
Step-by-step explanation:
To find the zeros of f(x) = x^3 + 5x^2 - 41x - 45, we are given that x + 9 is a factor of f(x). This means that if we substitute -9 for x, the equation will equal to zero. So, we can set up an equation:
0 = (-9)^3 + 5(-9)^2 - 41(-9) - 45
Simplifying this equation, we get 0 = -729 + 405 + 369 - 45 = 0
Therefore, -9 is a zero of f(x).