Question

Classify the following expression by degree and term: (2 points) x2y − 7xy + xyz + x

Answer 1

The degree of the expression is based on the term with the highest exponent. First we can simplify the expression because x2y and 7xy are like terms. You can rearrange x2y into 2xy (the arrangement will not change the product). So if you combine the like terms, you will have a new equation with only three terms, so it will be considered as a trinomial. 

xyz - 5xy + x

Remember to always arrange terms in your polynomial in descending order according to the degree. 

Now for degree, just get the sum of the exponents to determine the highest degree. The first term in the new equation has 3 variables, x,y, and z. Each of them, even when the power is not expressed are each raised to the power of 1. There are three variables so it will be:
1+1+1 = 3

The first term is classified as 3rd degree, which is the highest. So  now you can conclude that this expression is a 3rd degree trinomial.