In Exercises 35–36, use the Rational Zero Theorem to list all pos...

Question

In Exercises 35–36, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x) = x^4 - 6x^3 + 14x^2 -14x + 5

Accepted Answer

Hi there. This problem tells us to find all possible rational zeros for the given function for X to the fourth minus two. X third plus 10. X squared minus eight. X plus one. Using the rational zero through the rational zero theorem states that we have a fraction plus or minus factors of P defined by factors of Q. Where P is the coefficient at the end of our polynomial. So in this case our P is our very last number, which is what And Q is the coefficient of the highest degree in our polynomial. So highest degree is four, says the coefficient of this. X the fourth which is four. Now we can go ahead and find the factors of P. And the factors of Q. Well, the fact is of P Are the factors of one which is just one and 1. The factors of Q. The factors of four. Well we can have one in four and we can have two and two. So we're gonna use these numbers to create our fraction. Sir possible factors will be plus or minus. We have one on the top. R r p r p is always going to be one in this case let's say we use one first for the Q on the bottom Plus or -1/2. Where are other factor of cute and plus or minus 1/4. For other factor of Q. So these are all of our possible factors Are possible rational zeros of the function plus or -1/1. Plus or minus 1/2 plus or minus 1/4. Just one quick thing to note this. Plus or -1/1 can also simplify as just being plus or -1 many of that. Our answer. It's answer. B. Alright. I hope to help you solve the problem. Thank you for watching. Goodbye.

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