Find a polynomial function of degree 3 such that f (2) = 24 and x - 1, x and x + 2

are factors of the polynomial.

f (x) = 3x³ + 3x² - 6x

given the factors of the polynomial, then

f (x) = ax (x - 1) (x + 2) (a is a multiplier)

to find a use f (2) = 24

f (2) = 2a (1) (4) = 24 ⇒8a = 24 ⇒ a = 3, thus

f (x) = 3x (x² + x - 2) = 3x³ + 3x² - 6x