If the zeros of f(x) are -3, -2, and -1, then we can write this information as:
x = -3
x = -2
x = -1
Add 3, 2, and 1 respectively to each of these equations:
x + 3 = 0
x + 2 = 0
x + 1 = 0
Multiply the left-hand sides as factors:
(x+3)×(x+2)×(x+1)
NOTE:
If x equals any of the given values, the above expression will be zero.
If you multiply this expression to expand it, you will see that the coefficient of the x^3 term is 1.
Since the leading term is x^3, you have a third-degree polynomial.
f(x) = (x+3)(x+2)(x+1)
Mission accomplished.
