Which is not a possible rational zero of the function g(x) = 3x3 + 2x2 - 7x - 6?
There are infinitely many of them.
Are you given a list of choices?
All rational roots p/q will have
p is a factor of 6
q is a factor of 3
Any fraction not satisfying those conditions is not a possible rational root of g(x)
To find the possible rational zeros of the function g(x) = 3x^3 + 2x^2 - 7x - 6, we need to consider the factors of the constant term (-6) divided by the factors of the leading coefficient (3).
First, let's list the factors of -6: ±1, ±2, ±3, ±6.
Then, let's list the factors of 3: ±1, ±3.
Now, we need to find the rational zeros by taking the ratio of the factors of the constant term to the factors of the leading coefficient.
Possible rational zeros of the function are:
±1/1, ±2/1, ±3/1, ±6/1, ±1/3, ±2/3, ±3/3, ±6/3.
Simplifying these expressions gives us:
±1, ±2, ±3, ±6, ±1/3, ±2/3, ±1, ±2.
Therefore, all of these numbers are possible rational zeros except for ±1 and ±2.
To determine the possible rational zeros of a function, we can use the Rational Root Theorem. According to the theorem, if a rational number r is a zero of a polynomial function, then it must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is -6 and the leading coefficient is 3. We need to find the factors of these values.
The factors of -6 are ±1, ±2, ±3, and ±6.
The factors of 3 are ±1 and ±3.
To determine the possible rational zeros, we combine the factors in all possible combinations. We can write them in the form of p/q and check if any of them are zeros of the function.
The possible rational zeros of g(x) = 3x^3 + 2x^2 - 7x - 6 are:
±1/1, ±2/1, ±3/1, ±6/1, ±1/3, ±2/3, and ±6/3.
To answer the question, we need to find the option that is not a possible rational zero.