We can categorize polynomials based on two characteristics that every polynomial has:  degree, and number of terms.

Definition:  The degree of a polynomial is the highest degree of any of its terms.  Remember that the degree of a term is the sum of the exponents acting on the term’s variables.

Let’s look at two charts that will help us name certain polynomials:

To name a polynomial, simply find the name for its degree, find the name for the number of terms it has, and you’re done.  It’s that easy.  Let’s try some examples.

Example:  Name each polynomial by degree and number of terms

1. \( - {n^3}\)
2. \( - 5\)
3. \(1\)
4. \(6{x^4} + {x^3} + 9x\)

Solution:

1. The degree is 3, and the number of terms is 1.  This is a cubic monomial.
2. The degree is 1 (since no exponent shown means an exponent of 1) and the number of terms is 1.  So this is a constant monomial.
3. The degree is 1 (for the same reason as in 2.) and the number of terms is 1.  Again, we have a constant monomial.
4. The degree is 4 (highest degree on a term) and the number of terms is 3.  This is a quartic trinomial.

Below you can download some free math worksheets and practice.