Question

Explain what terms and degrees are and how. How are they used to classify polynomials? Also explain why this polynomial (4x2y + 5xy) is classified as a 3rd degree binomial?

Answer 1

When a polynomial has more than one variable, we need to look at each term. Terms are separated by + or - signs. Find the degree of each term by adding the exponents of each variable in it. The degree of the polynomial is found by looking at the term with the highest exponent on its variables.

Polynomials can be classified in two different ways - by the number of terms and by their degree. A monomial is an expression with a single term. It is a real number, a variable, or the product of real numbers and variables. A polynomial is a monomial or the sum or difference of monomials. A polynomial can be arranged in ascending order, in which the degree of each term is at least as large as the degree of the preceding term, or in descending order, in which the degree of each term is no larger than the degree of the preceding term. 

The polynomial $(4x^2y + 5xy)$ is classified as a 3rd degree binomial, because the monomial $4x^2y$ has degree equal to 3 and the monomial 5xy has degree equal to 2. The highest degree is 3, therefore the polynomial $(4x^2y + 5xy)$ is classified as a 3rd degree polynomial. Since polynomial  $(4x^2y + 5xy)$ has two terms, then it is classified as binomial.