1. Explain a method of determining the correct degree and classification of a polynomial.

2. Why is the polynomial, 4x^2y + 5xy classified as a 3rd degree binomial?

A polynomial can be classified according to the number of expressions that it has in a given equation. A monomial has only one expression having a coefficient (number) and a variable (letter). A binomial has two expressions, same as the definition of the monomial. And a trinomial has three expressions, same as the definition of a monomial. We can determine the degree of a polynomial by looking at the exponents of the given polynomial. If an expression has two variables with different exponents, you can add their exponent to determine their degree.

So the polynomial, 4x ²y + 5xy is classified as a 3rd degree binomial because the first term, 4x²y has a variables x² and y. The x² has an exponent 2 and y has an exponent 1. Adding the two makes it three.