Question

Which of the following equations represents the polynomial function with zeros 5, negative start fraction one over two end fraction, and −3, and a y-intercept of 15?

A. y = 2(x-5)(x+1/2)(x+3)
B. y = -(x+5)(2x-1)(x-3)
C. y = (x+5)(2x-1)(x-3)
D. y = -(x-5)(2x+1)(x+3)

Answer 1

D. y = -(x-5)(2x+1)(x+3)

Explanation:

"r" is a zero of the polynomial when (x -r) is a factor.

The three given zeros mean that (x -5), (x -(-1/2)), and (x -(-3)) will be factors of the equation. The product of the constants in these binomials (and any vertical scale factor) must be equal to the y-intercept.

For some scale factor "a", we want ...

(a)(-5)(1/2)(3) = 15

a = 15/(-7.5) = -2

and the desired polynomial function is ...

y = -2(x -5)(x +1/2)(x +3 = -(x -5)(2x +1)(x +3) . . . . matches choice D

______

Comment on the answer choices

It's all about the details. The various answer choices differ in various signs, so you need to pay attention.