Find the degree of this polynomial. \( -4 x^{3} y^{3} z^{4}+x^{6} y z^{2}-x^{3} y z^{5}-3 x y^{2}+y \) Submit

To find the degree of the polynomial \[ -4 x^{3} y^{3} z^{4} + x^{6} y z^{2} - x^{3} y z^{5} - 3 x y^{2} + y, \] we need to determine the degree of each term in the polynomial and then find the highest degree among them. 1. For the term \(-4 x^{3} y^{3} z^{4}\): - The degree is \(3 + 3 + 4 = 10\). 2. For the term \(x^{6} y z^{2}\): - The degree is \(6 + 1 + 2 = 9\). 3. For the term \(-x^{3} y z^{5}\): - The degree is \(3 + 1 + 5 = 9\). 4. For the term \(-3 x y^{2}\): - The degree is \(1 + 2 = 3\). 5. For the term \(y\): - The degree is \(1\). Now, we compare the degrees of all the terms: - The degrees are \(10\), \(9\), \(9\), \(3\), and \(1\). The highest degree among these is \(10\). Thus, the degree of the polynomial is \[ \boxed{10}. \]