Answer:
f(x) = x³ - x² - 6x
Step-by-step explanation:
If a polynomial f(x) has roots x = a and x = b then the factors are
(x - a) and (x - b) and the polynomial is the product of the factors, that is
f(x) = (x - a)(x - b)
Here the roots are x = 3, x = - 2 and x = 0, thus
(x - 3), (x - (- 2)) and (x - 0) are the factors, that is
(x - 3), (x + 2) and x , hence the polynomial is
f(x) = x(x - 3)(x + 2) ← expand the pair of factors
= x(x² - x - 6) ← distribute parenthesis by x
= x³ - x² - 6x
