List all of the possible rational zeros of f(x)= 3x^5 - 7x^3 + 2x - 15.
p= factor of 15
q= factor of 3
1,3,5,15
1,3
answer is 1,3,5,15,1/3,1,5/3,5
To find the possible rational zeros of a polynomial function, you can use the Rational Root Theorem. According to the theorem, the possible rational zeros of a polynomial are all the numbers that can be obtained by dividing a factor of the constant term (in this case 15) by a factor of the leading coefficient (in this case 3).
So, let's find the factors of both 15 and 3:
Factors of 15: 1, 3, 5, 15
Factors of 3: 1, 3
Now, considering the possible combinations of these factors, we can write the possible rational zeros as follows:
1/1, 1/3, 5/1, 5/3
But remember, we can simplify these fractions:
1/1 = 1
1/3 = 1/3
5/1 = 5
5/3 = 5/3
Thus, the possible rational zeros of the given polynomial function, f(x), are 1, 1/3, 5, and 5/3.