iven the polynomial g(x)

Question

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=−5
x equals negative 5

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

x=7
x equals 7

x=−7

Answer 1

To find which of the given responses is a zero of the polynomial \( g(x) = (x - 7)(3x - 5) \), we can apply the Factor Theorem, which states that if \( (x - c) \) is a factor of a polynomial, then \( c \) is a zero of the polynomial.

From the factors provided:

1. \( x - 7 = 0 \) gives us \( x = 7 \).
2. \( 3x - 5 = 0 \) gives us \( 3x = 5 \) or \( x = \frac{5}{3} \).

Now, let's evaluate the possible responses:

• \( x = -5 \): Not a zero
• \( x = -\frac{5}{3} \): Not a zero
• \( x = 7 \): This is a zero
• \( x = -7 \): Not a zero

Therefore, the correct answer is:

x = 7