The degree of a polynomial is determined by the highest sum of the exponents of its variables in each term of the polynomial. In this case, we have the polynomial 4xy + 11y + 3.
Let’s break it down term by term:
- For the first term, 4xy: The exponent of x is 1 and the exponent of y is also 1. Therefore, the sum of the exponents is 1 + 1 = 2.
- For the second term, 11y: The variable y has an exponent of 1, and since there is no x in this term, the total is simply 1.
- For the last term, 3: This is a constant term, which can be considered to have an exponent of 0. Thus, its degree is 0.
Now, we compare the degrees of all the terms:
- The degree of 4xy is 2.
- The degree of 11y is 1.
- The degree of 3 is 0.
Since the degree of the polynomial is defined as the highest degree among its terms, we find that the highest degree is 2. Therefore, the degree of the polynomial 4xy + 11y + 3 is 2.