Roman C. answered • 04/26/13

Masters of Education Graduate with Mathematics Expertise

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, 3x^{2}y^{3}, and -7xz are all valid terms.

Examples of terms that are not allowed:

6x^{-5}y ← Violates condition 3 because the exponent -5 is negative.

4x^{2/3} ← Violates condition 3 because the exponent 2/3 is not an integer.

x^{y} or 2^{y} ← Violates condition 3 because the exponent y is not a constant.

Here are a few examples of polynomials:

x^{2}

5xy^{2} - 6z^{3}

x^{2 }+ y^{2}

etc.

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 x^{3}y^{7}z^{2} has degree 3+7+2 = 12.

A polynomials degree is just the largest of the degrees of the terms.

For example, x^{3} + y^{2}z^{4} + 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.