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)

Question

1. x= - 5/3
2. x= -5
3. x= 7
4. x= -7

Answer 1

To find the zero of a polynomial using the Factor Theorem, we set the polynomial equal to zero and solve for x.

In this case, the polynomial g(x) is given as (x - 7)(3x - 5). Setting it equal to zero, we have:

(x - 7)(3x - 5) = 0

Now we can apply the Zero Product Property, which states that if a product of factors equals zero, then at least one of the factors must equal zero. Therefore, we can set each factor equal to zero and solve for x:

x - 7 = 0 --> x = 7

3x - 5 = 0 --> 3x = 5 --> x = 5/3

Therefore, the zeros of g(x) are x = 7 and x = 5/3. However, neither of these options is listed in the given choices. Therefore, the answer is none of the above.