Question

select the correct answer.
if the factors of quadratic function g are (x - 7) and (x + 3), what are the zeros of function g?
a. -7 and -3
b. -3 and 7
c. -7 and 3
d. 3 and 7

Explanation:

Step1: Recall zero - factor property

The zero - factor property states that if \((x - a)\) is a factor of a polynomial, then \(x=a\) is a zero of the polynomial. For a factor \((x - c)\), we set \(x - c = 0\) and solve for \(x\) to find the zero.

Step2: Find zero for factor \((x - 7)\)

Set \(x-7=0\). Solving for \(x\), we add 7 to both sides of the equation: \(x=7\).

Step3: Find zero for factor \((x + 3)\)

Rewrite \((x + 3)\) as \((x-(- 3))\). Using the zero - factor property, set \(x+3 = 0\). Subtract 3 from both sides of the equation: \(x=-3\).
So the zeros of the function \(g\) are \(x = 7\) and \(x=-3\) (or - 3 and 7).

Answer:

B. -3 and 7