In Exercises 1–8, use the Rational Zero Theorem to list all possi...

Question

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=x^5−x^4−7x^3+7x^2−12x−12

Accepted Answer

list the possible rational zeros of the following function using the rational zero theorem. And we have this function here. The rational zero theorem states that are possible zeros are given by the ratio plus or minus P over Q. Where p is our constant and our polynomial Usually this is the very last term. So in this case it will be our 16. The Q is our leading coefficient. The leading coefficient is the number in front of the highest exponent. So we look here, RP is on a constant which is R. Q. Which is the leading coefficient would be the three that is in the very front of the polynomial. Now we can set up a ratio. So you want to take the factors of P and the factors of Q. So factors of P Will be the factors of 16. That would be 1, 16 To an eight and 4 and four. Now the factors of Q. That would be three. So just be one and 3. Now we can set up our ratio but we will have plus or minus now P is on top. So let's say we have 1/1, 2/1 for over one. 8/1 and 16/1 plus or minus on all of them. That did the same thing for our Q equaling three. We have plus or minus number three plus or minus 2/ plus or minus 4/3 plus or minus 8/ and plus or minus 16/3. We can do some simplification. We get plus or minus one plus or minus two plus or minus four plus or minus eight plus or minus 16 plus or minus one third plus or minus two thirds plus or minus four thirds plus or minus eight thirds and finally plus or minus 16 3rd. That's the process. We can simplify, which means these are all of our possible rational zeros. Now, if you look over we can see that this answer is answer B. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=x^5−x^4−7x^3+7x^2−12x−12