In Exercises 1–4, is the algebraic expression a polynomial? If it...

Question

In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. (2x+3)/x

Accepted Answer

Hi there this problem says the right list. Their form of the polynomial. After verifying that the given algebra expression is a polynomial. So this polynomial we have here is x squared plus three X plus two. Now we have a few checks for a polynomial. The first step down the stairs form of a polynomial. This is given by F X equals a. It's city in plus B X. To the n minus one plus C X. The n minus two, two. And so on. Until we get to the end of our polynomial where A, B, C and so on are real numbers. So that is our first take, our next check is you want to see if n is a positive imager? So for every expert that we have we want to see if it's a positive energy. So every exponent has to be a possibility everything be positive. So let's go ahead and apply these checks to our polynomial. Our potential polynomial rather X squared plus three X plus two. So we look at it. Here we are in the form X at the end plus bx n minus one plus c x, n minus two. Are in here is actually to our first name. So we're going down we don't see any negative exponents. All of our exponents are positive. So it passes that check and and as a positive manager. So based on all the information we have here we can conclude that this is indeed a polynomial with degree to even. Okay, thank you for watching to help you solve the problem. Goodbye

In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. (2x+3)/x

Key Concepts

Polynomial Definition

Standard Form of a Polynomial

Rational Expressions

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