A polynomial is a sum of terms where the terms must satisfy the following
1. A constant is a valid term.
2. Other terms must be a constant times a product of powers of variables.
3. The exponents must be positive integer constants.
For example 2, 3x2y3, and -7xz are all valid terms.
Examples of terms that are not allowed:
6x-5y ← Violates condition 3 because the exponent -5 is negative.
4x2/3 ← Violates condition 3 because the exponent 2/3 is not an integer.
xy or 2y ← Violates condition 3 because the exponent y is not a constant.
Here are a few examples of polynomials:
5xy2 - 6z3
x2 + y2
Note: If a term is subtracted then that is the same as adding a term with the opposite sign.
The degree of a term is the sum of the exponents. Here, if a variable is written without an exponent, it's exponent is 1. A constant term's degree is 0.
For example 2xy has degree 1+1 = 2. and x3y7z2 has degree 3+7+2 = 12.
A polynomials degree is just the largest of the degrees of the terms.
For example, x3 + y2z4 + 3 has three terms with respective degrees 3, 6, 0.
Thus this polynomial's degree is the largest of these three values, which is 6.