In Exercises 1–10, determine which functions are polynomial funct...

Question

In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. h(x)=7x^3+2x^2+1/x

Accepted Answer

Welcome back. I'm so glad you're here. We are given this function F. Of X equals nine X to the fifth plus five X to the fourth plus three over X. And we are asked to determine whether or not this function is a polynomial and if it is a polynomial, what is its degree? Well, in order to determine whether it's a polynomial, we're going to be looking at all of the exponents and I want to get this X out of the denominator of the fraction three over X in order to look at its exponents. So I'm going to bring down the nine X to the fifth plus five X to the fourth. And we're going to look at this X in the denominator it's got an exponent of one. But in order to bring it up to the numerator, we recall from previous lessons that we need to flip the exponents sign. So this is no longer going to be plus three over X. It's now going to be plus three times X to the negative first because we've flipped its sign. And now we can begin to ask our questions of whether or not this is a polynomial. The first question we ask is are all of the exponents positive integers and our exponents here are 54 and negative one. Well five and four are positive but negative one is not. So we can stop right here at our first question because we know that no, this is not a polynomial function. So that matches with answer choice D. Well done. We'll catch you on the next one

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In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. h(x)=7x^3+2x^2+1/x

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