State the degree of the following polynomial 9x^4y^3+6xy-3y

This is a polynomial

9x^4y^3+6xy-3y

These are the terms of the polynomial
9x^4y^3
6xy
-3y

x, y are the variables of the first term.

4 is the degree of x in the first term, and
3 is the degree of y in the first term.

Therefore the degree of the first term
9x^4y^3
is the sum of the degrees of all the variables of the term (x and y) = 4+3=7

The degree of the polynomial is the highest degree among all the terms.
So you need to calculate the degree of each term, the highest degree is the degree of the polynomial.

To determine the degree of a polynomial, we need to find the highest exponent of the variables in the polynomial.

In the given polynomial 9x^4y^3 + 6xy - 3y, the first term is 9x^4y^3. The exponent of x is 4, and the exponent of y is 3.

The degree of a term is obtained by adding the exponents of the variables in that term. In this case, the degree of the term 9x^4y^3 is 4 + 3 = 7.

Next, we look at the other terms in the polynomial. The second term is 6xy. The exponent of x is 1, and the exponent of y is 1. Thus, the degree of the term 6xy is 1 + 1 = 2.

Lastly, we have the term -3y. The exponent of y in this term is 1, so the degree is 1.

Now, we compare the degrees of the terms to determine the degree of the polynomial. The highest degree among the terms is 7. Therefore, the degree of the polynomial 9x^4y^3 + 6xy - 3y is 7.