degree of algebraic terms

Question

In SCHAUM’S Easy OUTLINES PRECALCULUS book example 1.7(e) it says x³y²-30x⁴ has a degree of 5.

It says:

The degree of a term in a polynomial is the exponent of the variable, or,
if more than one variable is present, the sum of the exponents of the variables.
The degree of a polynomial with more than one term is the largest of
the degrees of the individual terms.

So my question is, if x⁴ is larger than x³, why isn't x⁴ used with y² to make a degree of 6 instead of 5

Answer 1

The polynomial you gave has two terms: the first is x³y², and the second is -30x⁴. Using the definition you gave, the degree of the first term, x³y², is 3 + 2 = 5, while the degree of the second term, -30x⁴, 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 y² of the first term and the x⁴ 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!