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)
To apply the Factor Theorem, we need to find a value of x that makes g(x) equal to zero.
Since g(x) is equal to zero when (x-7) equals zero or when (3x-5) equals zero, we want to solve the equations (x-7)=0 and (3x-5)=0.
For the equation (x-7)=0, adding 7 to both sides gives us x=7.
For the equation (3x-5)=0, adding 5 and then dividing by 3 gives us x=5/3.
Therefore, the zeros of g(x) are x=7 and x=5/3.
None of the answer choices are correct, so we need additional information to determine the correct answer.
To determine the zero of a polynomial using the Factor Theorem, we need to find a value of x that makes the polynomial equal to zero.
In this case, the factored form of g(x) is given as g(x) = (x - 7)(3x - 5).
To find a zero, we set g(x) equal to zero:
0 = (x - 7)(3x - 5).
To find the values of x that make this equation true, we need to solve for x.
Setting each factor equal to zero, we have:
x - 7 = 0 or 3x - 5 = 0.
Solving these equations, we find:
x = 7 or x = 5/3.
Therefore, both x = 7 and x = 5/3 are zeroes of g(x).