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)
1. x= - 5/3
2. x= -5
3. x= 7
4. x= -7
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.
To find the zero of a polynomial using the Factor Theorem, we need to set the polynomial equal to zero and solve for x.
Given that g(x) = (x-7)(3x-5), we set it equal to zero:
(x-7)(3x-5) = 0
Now we can use the Zero Product Property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.
Considering each factor separately:
1) x-7 = 0
x = 7
2) 3x-5 = 0
3x = 5
x = 5/3
Therefore, the zeros of g(x) are x = 7 and x = 5/3.
None of the options provided -5, -5/3, and -7 - match the zeros of g(x).
To apply the Factor Theorem and find the zeros of the polynomial g(x)=(x−7)(3x−5), we need to find the values of x that make the polynomial equal to zero.
According to the Factor Theorem, if a polynomial g(x) can be factored as (x−a)(b−x), then a zero of the polynomial is x=a. In other words, if g(a) = 0, then a is a zero of g(x).
In this case, the factored form of g(x) is (x−7)(3x−5). To find the zeros, 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 and 3x−5 = 0
Solving these equations, we find:
x = 7 and x = 5/3
Therefore, the zeros of g(x) are x = 7 and x = 5/3.
From the answer choices given:
1. x= -5/3: This is not a zero of g(x).
2. x= -5: This is not a zero of g(x).
3. x= 7: This is a zero of g(x) because it satisfies g(7) = 0.
4. x= -7: This is not a zero of g(x).
So, the correct answer is option 3: x = 7.