As a math tutor, you deal with polynomials half the weeks of the year.

A polynomial is an expression in which the variables can have only positive, whole-number exponents.  Examples of polynomials are 3x⁷-12x⁵+1 or  -2x – 12.

In a polynomial, terms are separated by plus or minus signs.  Therefore, 7x – 12 has two terms, whereas  -13x⁷yz² has only one.

Polynomials are often named by how many terms they have, as follows:

7x²                   One term: monomial

3x – 12             Two terms: binomial

-4x⁴ + 3x -5     Three terms: trinomial

A polynomial with more than three terms is just called a polynomial.

Consider the following monomial:

-11x⁵

-11 is called the coefficient.  x is called the variable.  5 is the exponent.

The degree of a polynomial is the highest exponent found in one of its terms.  For example, 5x³ has degree 3. The trinomial

x⁷ + 3x³ – 12

has degree 7.

The constant term of a polynomial is the term with no variable attached. In 3x – 12, the constant term is -12.

There are two facts about polynomials that might be a little surprising:

Fact 1:

A constant term has degree zero.  Reason: x⁰= 1 by definition. The result:

3x⁰ = 3(1) = 3.

We just write 3, but the degree of the term is still zero.

Fact 2:

If the coefficient is not written, it is 1.  Reason: x⁵ = 1x⁵.

There are a couple of finer points, but the above is good for a start.  Much more will be said about polynomials in future posts.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.