Find the zeros of the following polynomial p (x) = 3x³ + 9x² - 12x

x = - 4, x = 0, x = 1

Step-by-step explanation:

To find the zeros equate p (x) to zero, that is

3x³ + 9x² - 12x = 0 ← divide through by 3

x³ + 3x² - 4x = 0 ← factor out x from each term

x (x² + 3x - 4) = 0

x (x + 4) (x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x = 0

x + 4 = 0 ⇒ x = - 4

x - 1 = 0 ⇒ x = 1