Given 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=−7
x equals negative 7

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

x=7

Answer 1

To find the zeros of the polynomial \( g(x) = (x - 7)(3x - 5) \) using the Factor Theorem, we set each factor equal to zero and solve for \( x \).

1. From the first factor: \[ x - 7 = 0 \implies x = 7 \]

2. From the second factor: \[ 3x - 5 = 0 \implies 3x = 5 \implies x = \frac{5}{3} \]

Now, we evaluate the provided options for zeros:

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

Thus, the zero of \( g(x) \) is:

x = 7.