can some one please help figure this problem out

Determine whether each expression is a polynomial.If it is a polynomial, state the degree of the polynomial.
5x^3+2xy^4+6xy

can someone please help me

Yes, I can help you with that problem. To determine whether an expression is a polynomial, we need to check if it meets two criteria:

1. All the terms should have non-negative integer exponents.
2. The coefficients should be real numbers.

Let's break down the given expression to analyze it:

5x^3 + 2xy^4 + 6xy

The first term, 5x^3, has a non-negative integer exponent (3) and a real coefficient (5), so it satisfies the criteria.

The second term, 2xy^4, has mixed variables (x and y) and one non-negative integer exponent (4), so it also satisfies the criteria.

The third term, 6xy, has mixed variables (x and y) but no exponent. However, we can assume it has an exponent of 1 (which is equivalent to having no exponent). The coefficient, 6, is a real number. Therefore, it also satisfies the criteria.

Since all the terms in the expression satisfy the criteria, we can conclude that the given expression, 5x^3 + 2xy^4 + 6xy, is indeed a polynomial.

To determine the degree of the polynomial, we need to identify the term with the highest total degree. The total degree of a term is the sum of the exponents of its variables.

In this case, the term with the highest total degree is 2xy^4, which has a total degree of 4 + 1 = 5.

Therefore, the polynomial 5x^3 + 2xy^4 + 6xy has a degree of 5.