Answer:
x = - 3, x = - 1, x = 6
Explanation:
given (x - a) is a factor of f(x) , then the remainder on dividing f(x) by (x - a) is zero.
using Synthetic division to divide f(x) by a = 6
6 | 1 - 2 - 21 - 18
↓ 6 24 18
--------------------------
1 4 3 0 ← remainder
quotient is x² + 4x + 3 = (x + 3)(x + 1)
then
f(x) = (x + 3)(x + 1)(x - 6)
to find the zeros , equate f(x) to zero , that is
(x + 3)(x + 1)(x - 6) = 0
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x + 1 = 0 ⇒ x = - 1
x - 6 = 0 ⇒ x = 6