Question

select the correct answer.
which function has zeros of -8, 1, and 3?
a. $y = (x - 3)(x + 8)(x - 1)$
b. $y = (x + 1)(x - 8)(x + 3)$
c. $y = x(x + 8)(x - 3)$
d. $y = x(x + 3)(x - 8)$

Explanation:

Step1: Recall Zero - Factor Property

If a function \(y = f(x)\) has a zero at \(x = a\), then \((x - a)\) is a factor of \(f(x)\).

Step2: Find Factors for Each Zero

• For the zero \(x=-8\), the factor is \((x - (-8))=(x + 8)\).
• For the zero \(x = 1\), the factor is \((x-1)\).
• For the zero \(x = 3\), the factor is \((x - 3)\).

So the function with zeros \(-8\), \(1\), and \(3\) should be \(y=(x - 3)(x + 8)(x - 1)\), which is option A.

Answer:

A. \(y=(x - 3)(x + 8)(x - 1)\)