1. Find the degree of the polynomial $4 x^{3} y-4 x y+2$.
A. 6
C. 2
B. 4
D. 3
Final Answer: The degree of the polynomial \(4 x^{3} y-4 x y+2\) is \(\boxed{4}\).
Step 1 :Find the degree of the polynomial \(4 x^{3} y-4 x y+2\).
Step 2 :The degree of a polynomial in two variables is the highest sum of the exponents in any term of the polynomial.
Step 3 :In this case, we need to find the highest sum of the exponents in the terms of the polynomial \(4 x^{3} y-4 x y+2\).
Step 4 :The exponents in the terms are [(3, 1), (1, 1), (0, 0)].
Step 5 :The sum of the exponents in each term gives the degrees [4, 2, 0].
Step 6 :The highest degree is 4.
Step 7 :Final Answer: The degree of the polynomial \(4 x^{3} y-4 x y+2\) is \(\boxed{4}\).