Question

The values in the table below were taken from the graph of a 3rd-degree polynomial function. x −2 −1 0 1 2 P(x) 0 18 12 0 0 Which of the following represents the equation of the polynomial function? (4 points)

ANSWERS:
P(x) = (x − 1)(x + 2)(x − 2)

P(x) = −3(x − 1)(x + 2)(x − 2)

P(x) = (x + 1)(x + 2)(x − 2)

P(x) = 3(x − 1)(x + 2)(x − 2)

Answer 1

From the given values, we see that P(x) = 0 at x = -2, x = 1, and x = 2. This means that P(x) has factors of (x + 2), (x - 1), and (x - 2). So we can assume that:
P(x) = k(x + 2)(x - 1)(x - 2). Then we substitute x = 0, which gives P(0) = 4k, and according to the given P(0) = 12, so this means that k = 3. So the equation is
P(x) = 3(x + 2)(x - 1)(x - 2), which is the fourth choice.