Final answer:
To factorize the cubic polynomial x³ - x² + 22x + 40 using the factor theorem, we need to find the factors that make the polynomial equal to zero. By trying values, we find that (x + 4) is a factor of x³ - x² + 22x + 40.
Step-by-step explanation:
To factorize the cubic polynomial x³ - x² + 22x + 40 using the factor theorem, we need to find the factors that make the polynomial equal to zero. The factor theorem states that if a polynomial f(x) has a factor (x - r), then f(r) = 0. Therefore, we can try different values of r and check if the polynomial equals zero. By trying values, we find that (x + 4) is a factor of x³ - x² + 22x + 40. Therefore, we can use synthetic division or long division to divide x³ - x² + 22x + 40 by (x + 4) to obtain the remaining quadratic factor.