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. f(x)=5x^2+6x^3

Accepted Answer

Welcome back. I'm so glad you're here. We are given this function F of X equals to X squared plus nine X. To the fourth. 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, when we're determining whether or not something is a polynomial, we're going to ask two questions. The first question is looking at the variables exponents we want to know are all of the exponents positive integers. So here we've got an X squared. So one exponents is the two and we have an X to the fourth. The other exponents is a four and two and four are both positive and two and four are both integers. Great. The first condition is met. So we can ask the second question. The second question is are all of the coefficients and constance real numbers? Well, our coefficients here are two and positive nine. We don't have any constants and two and nine are real numbers. So yes, both conditions are met. Yes, this is a polynomial. So now we ask ourselves what is the degree of this polynomial for the degree? We look at the value of all of our exponents and we're going to look for the exponent that has the highest value and in this case that is four and the degree is equal to the value of our highest valued exponent. So the degree to this problem is for we look at our answer choices and that matches with answer choice B. Well done. We'll catch 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. f(x)=5x^2+6x^3