Definitions

Before starting to explore any new topic, you need to first familiarize yourself with the terminology that will be used in the lessons. Make sure you are familiar with the terminology shown below before you move on to the rest of the lessons in this topic.

Term

A term is a symbol, or a number, or a group of symbols and numbers linked by multiplication and division. In an expression, multiple terms are seperated by addition and subtraction (plus and minus signs). For example, all of the following are single terms:

The following expression contains three separate terms:

Polynomial

A polynomial is an algebraic expression consisting of one or more terms. Certain polynomials have special, commonly used names as seen below:

• Monomial

  A monomial is an algebraic expression consisting of exactly one term. The following are all examples of monomials:

• Binomial

  A binomial is an algebraic expression consisting of exactly two terms. The following are all examples of binomials:

• Trinomial

  A trinomial is an algebraic expression consisting of exactly three terms. The following are examples of trinomials:

It is important to note that ALL OF THE ABOVE 'SPECIAL POLYNOMIALS' ARE POLYNOMIALS. We usually refer to a polynomial of MORE than three terms as a polynomial, but every example you see above is a polynomial as well as being a mono-, bi-, or trinomial.

Like Terms

Two (or more) terms are said to be 'like terms' if their variable part is EXACTLY the same. The 'variable part' of a term is everything that comes after the coefficient (or number part). For example:

2x² and 19x² ARE like terms. (The variable part --> x² is exactly the same in both terms)

-3xy³ and 18xy³ ARE like terms. (The variable part --> xy³ is exactly the same in both terms.)

6 and 2 ARE like terms. (There is NO variable part in either term, which makes the variable part exactly the same.)

6x and 4x² are NOT like terms. (x and x² are different.)

10xyz and 10x²yz are NOT like terms. (They have variable parts that are similar, but not EXACTLY the same.)

Now that you have explored some of the more important definitions, you can head back to the polynomials main page or you can try some sample questions.