 In this video, we provide the solution to question number 4 from the practice exam number 3 for Math 1050. We're given a polynomial function f of x equals 3x to the fourth minus 7x cubed plus 5x plus 4. And so we're supposed to then list all of the possible rational roots of this polynomial. That is to say we're supposed to invoke the rational roots theorem to determine what these possible rational roots are. To do this, we take the constant term of the polynomial, which is positive 4. We take the leading coefficient, which is positive 3, and we look at all possible divisors of 4 divided by 3. That is, what are the divisors of 4? What are the divisors of 3? So we look at all these possible rational expressions, p and q. So the divisors of 4, of course, are 1, 2, and 4. The divisors of 3 are 1 and 3, as it's a prime number. And so we have to consider positive and negative cases. So we're going to get plus or minus 1, plus or minus 2, plus or minus 4. So those are all the divisors of 4 if we divide by 1 here. Then we have to take all these same divisors and divide them by 3. So we get plus or minus 1 third, plus or minus 2 thirds, and plus or minus 4 thirds. So these 12 possibilities, because again we do consider positive and negative, these are the possible rational roots. And so then we see that list is exactly choice C, which is then the correct answer.