Recall from §2.2 that a polynomial in two variables x and y is an expression of the form...

Recall from §2.2 that a polynomial in two variables x and y is an expression of the form

where ckl can be any real number for 0 ≤ k, l ≤ d. The degree of the term and the degree of the polynomial p is the largest degree of any nonzero term of the polynomial (i.e., the largest degree of any term for which For example, the polynomial

has five terms of degrees 15, 5, 4, 4, and 0. The degree of p is therefore 15. (Note: The degree of the zero polynomial p(x, y) ≡ 0 is undefined.)

(c) Try to formulate and prove a conjecture relating the degree of a polynomial p to the degree of its partial derivatives.