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If the cubic function P(x) includes the points (1, 0), (3, 0), (−4, 0), and (0, 36), which of the following represents this function?

3(x − 1)(x − 3)(x + 4)
−3(x − 1)(x − 3)(x + 4)
−2(x + 1)(x + 3)(x − 4)
2(x + 1)(x + 3)(x − 4)

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Answer: choice #2, or −3(x − 1)(x − 3)(x + 4)

Explanation:

The first three points are zeros (or roots) of the polynomial  (1, 0), (3, 0), (−4, 0).

They imply factors (x-1), (x-3) and (x+4) and can be easily check against the factorized forms in the four choices. They allow us to narrow the choices to the first two.

Then we use the point (0,36), setting x=0 to determine the value y. In the first choice the value is -36, in the second choice it is 36, therefore the answer is choice #2.  

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