In math, there are some words that are practically foundations to everything else. Just like any topic, math has its own vocabulary and one of the first words you should get comfortable with in algebra is the word “polynomial”.

Polynomials are expressions involving terms which may have exponents that are multiplied, added, or subtracted from eachother. For example, each of the expressions below would qualify as a polynomial:

In each case above, notice that the exponents were POSITIVE INTEGERS (positive whole numbers). If an exponent is negative, then this implies you are dividing by that term (based on the definition of a negative exponent) and polynomials can not have any division involving the variables. A polynomial CAN have fractions involving just the numbers in front of the variables (the coefficients).

With that in mind, the following are NOT polynomials:

(negative exponent)

(fractional exponent)

There are a few special types of polynomials which get their own names. (Remember, we are thinking of a term as something like or 5):

• Monomial A monomial is a polynomial with one term:
• Binomial A binomial is a polynomial with two terms being added or subtracted:
• Trinomial A trinomial is a polynomial with three terms being added or subtracted:

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