Answer:
f(x) = x³ + 10x² + 27x + 18
Step-by-step explanation:
Given the zeros x = - 3, x = - 6 and x = - 1
Then the factors are (x + 3), (x + 6), (x + 1)
and the polynomial is the product of the factors, that is
f(x) = (x + 3)(x + 6)(x + 1) ← expand the first 2 factors using FOIL
= (x² + 9x + 18)(x + 1) ← distribute
= x³ + 9x² + 18x + x² + 9x + 18 ← collect like terms
= x³ + 10x² + 27x + 18
