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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