Question

which statement about g(x) = x² - 576 is true?
f the zeros, -288 and 288, can be found when 0 = (x + 288)(x - 288).
g the only zero, 288, can be found when 0 = (x - 288)².
h the zeros, -24 and 24, can be found when 0 = (x + 24)(x - 24).
j the only zero, 24, can be found when 0 = (x - 24)².
2
question text

Explanation:

Step1: Recall difference of squares

The function \( g(x) = x^2 - 576 \) is a difference of squares, since \( 576 = 24^2 \). The formula for difference of squares is \( a^2 - b^2=(a + b)(a - b) \). So, \( x^2 - 24^2=(x + 24)(x - 24) \).

Step2: Find the zeros

To find the zeros, set \( g(x)=0 \), so \( 0=(x + 24)(x - 24) \). Solving \( x + 24 = 0 \) gives \( x=-24 \), and solving \( x - 24 = 0 \) gives \( x = 24 \). So the zeros are -24 and 24, which matches option H.

Answer:

H. The zeros, -24 and 24, can be found when \( 0=(x + 24)(x - 24) \).