Question

Given the polynomial g(x)
in its factored form as shown here: g(x)=(x−7)(3x−5)
, apply the Factor Theorem. Which of the following is a zero of g(x)
?(1 point)
Responses

x=−53
x equals negative Start Fraction 5 over 3 End Fraction

x=7
x equals 7

x=−7
x equals negative 7

x=−5

Answer 1

To determine which of the provided options is a zero of the polynomial \( g(x) = (x - 7)(3x - 5) \), we apply the Factor Theorem. According to the Factor Theorem, if \( x - c \) is a factor of the polynomial \( g(x) \), then \( c \) is a zero of \( g(x) \).

Let's examine the factors of \( g(x) \):

1. From the factor \( (x - 7) \), we can see that when \( x = 7 \):
\[
g(7) = (7 - 7)(3(7) - 5) = 0 \cdot (21 - 5) = 0
\]
Thus, \( x = 7 \) is a zero of \( g(x) \).

2. From the factor \( (3x - 5) \), we can find the zero by setting \( 3x - 5 = 0 \):
\[
3x - 5 = 0 \implies 3x = 5 \implies x = \frac{5}{3}
\]
This means \( x = \frac{5}{3} \) is also a zero of \( g(x) \).

Now, let’s review the options given:
- \( x = -\frac{5}{3} \)
- \( x = 7 \)
- \( x = -7 \)
- \( x = -5 \)

The correct answer from these responses is:
**x = 7**.