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=−5 x equals negative 5 x=−53 x equals negative Start Fraction 5 over 3 End Fraction x=−7 x equals negative 7 x=7

Answer 1

To find the zeros of the polynomial \( g(x) = (x - 7)(3x - 5) \) using the Factor Theorem, we need to set \( g(x) = 0 \) and solve for \( x \).

1. Set each factor equal to zero:
- For the first factor: \( x - 7 = 0 \)
\[
x = 7
\]

- For the second factor: \( 3x - 5 = 0 \)
\[
3x = 5 \implies x = \frac{5}{3}
\]

So, the zeros of \( g(x) \) are \( x = 7 \) and \( x = \frac{5}{3} \).

Among the options provided:
- \( x = -5 \) (not a zero)
- \( x = -\frac{5}{3} \) (not a zero)
- \( x = -7 \) (not a zero)
- \( x = 7 \) (this is a zero)

The correct response is **\( x = 7 \)**.