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)?
x=7
x equals 7

x=−5
x equals negative 5

x=−7
x equals negative 7

x=−53

Answer 1

The zero or root of a polynomial is the value of x that makes the polynomial equal to zero.

Using the Factor Theorem, if x-a is a factor of a polynomial function, then f(a) = 0.

In this case, g(x) = (x-7)(3x-5). To find a zero of g(x), we need to find a value of x that makes g(x) equal to zero.

Setting g(x) equal to zero, we have:
(x-7)(3x-5) = 0

To find the zeros, we set each factor equal to zero:
x-7 = 0 --> x = 7
3x-5 = 0 --> 3x = 5 --> x = 5/3

Therefore, x = 7 and x = 5/3 are zeros of g(x).

Out of the given options, x=7 is the zero of g(x).