Identify each expression as a polynomial or not a polynomial. For...

Question

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. 15a^2b^3+12a^3b^8-13b^5+12b^6

Accepted Answer

Hello. Today we're going to be determining whether the given expression is a polynomial or not. So in order for this to be a polynomial, every exponent within the expression must be a positive integer. In the first term we are given exponents three and five. The second term has exponents six and eight. The third term has the exponent of seven and the fourth term has the exponent of four. All of these classify to be positive integers and with that being said this is going to be a polynomial. So now that we know that this is a polynomial, we need to indicate its degree and we need to classify the polynomial based off with a number of terms. So let's go ahead and start with the classification. A mono meal is an expression that has one term. A binomial is an expression that has two terms And the tri no meal has an expression that has three terms if what's given to us doesn't match these three criteria. We're going to classify it as none of these but currently there are four terms given to us in this expression we have 1234 positive terms and that doesn't match the criteria for mono meal binomial or try no meal. So the classification for this is going to be none of these. And finally let's go ahead and determine the degree of the polynomial. The degree is the value of the highest exponent. However, the 1st and 2nd term of this expression Have more than one exponent. So in order to determine the degree we're going to need to add the values of the exponents together. So in the first term, if we add three and five together, we're going to get to, we're going to get an expression of eight. And in the second term, if we add six and eight together we get 14 and 14 is the highest value for the exponents. So the degree of this polynomial is going to be 14. So just to review what we discovered this is a polynomial, it doesn't classify as a mono meal, binomial or try no meal because it has four terms and its degree is 14. With that being said, the answer to this problem is going to be C. So I hope this video helps you in understanding how to approach this problem and I'll go ahead and see you all in the next video.

Struggling with College Algebra?

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. 15a^2b^3+12a^3b^8-13b^5+12b^6

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