Christopher G. answered • 08/07/13

Math Tutor - Algebra, Trig, Calculus, SAT/ACT Math

The polynomial you gave has two terms: the first is x^{3}y^{2}, and the second is -30x^{4}. Using the definition you gave, the degree of the first term, x^{3}y^{2}, is 3 + 2 = 5, while the degree of the second term, -30x^{4}, is 4. Therefore, the degree of the entire polynomial is 5.

The definition says that the degree of a polynomial is the largest of the degrees of the **individual terms**; you can't simply add the highest term of each *variable* in each term. You're thinking of taking the y^{2} of the first term and the x^{4} of the second and making that the total degree, but you can't separate terms like that to find the degree. I think what might be throwing you off is that there are two separate *variables* here, the x and the y, and you're trying to find the highest power of each of them instead of the individual *terms*.

Hope this helps!