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)
x = -5/3
x = 7
x = -5
x -7
The Factor Theorem states that if a polynomial g(x) is divided by x-a, where a is a number, and the remainder is zero, then a is a zero of g(x).
In this case, g(x) = (x-7)(3x-5). To find the zeros of g(x), we set g(x) equal to zero and solve for x:
(x-7)(3x-5) = 0
Setting each factor equal to zero, we have:
x-7 = 0 --> x = 7
3x-5 = 0 --> 3x = 5 --> x = 5/3
Therefore, the zero of g(x) is x = 7.
To apply the Factor Theorem, we need to find values of x that make g(x) equal to zero.
Given the factored form of g(x), g(x) = (x - 7)(3x - 5).
To find the zeros, we set g(x) equal to zero:
(x - 7)(3x - 5) = 0.
Now we can solve for x:
x - 7 = 0 or 3x - 5 = 0.
Solving each equation:
For x - 7 = 0, we add 7 to both sides:
x = 7.
For 3x - 5 = 0, we add 5 to both sides and then divide by 3:
3x = 5;
x = 5/3.
Therefore, the zeros of g(x) are:
x = 7 and x = 5/3.
Hence, the correct answer is x = 7.