Question

Find a third–degree polynomial function such that f(0) = –12 and whose zeros are 1, 2, and 3. Using complete sentences, explain how you found it.

Answer 1

f(x) = 2(x-1)(x-2)(x-3)

Answer 2

the factors (x-1), (x-2), (x-3) are needed for the function to equal zero at x=1, 2, 3.

Answer 3

the 2 on the outside is needed because when x=0, the value of f must be -12:
-12 = k(0-1)(0-2)(0-3)
-12 = k(-1)(-2)(-3)
-12 = k (-6)
2 = k