- A term is a number, a variable, or a
product of numbers and variables.
- A monomial is a term in which the
variables are only raised to whole number powers.
- A polynomial is a monomial or sum of
- A monomial is a polynomial with only one
- A binomial is a polynomial with exactly
- A trinomial is a polynomial with exactly
- Polynomials dont, in the usual sense, have size (in
the way that numbers do, that is). Sometimes, however,
its necessary to compare the relative
sizes of two polynomials anyway. To do that,
we use the concept of degree.
- The degree of a term with just one
variable is the power to which the variable gets raised.
(This is 0 if there is no variable.)
- The degree of a polynomial is the
largest degree of any of its terms.
- It is common two write polynomials in decending powers of
the variable, or descending order. This
leads to two more pieces of vocabulary.
- The leading term of a polynomial is the
term with the highest degree.
- The leading coefficient is the
coefficient of the leading term.
- Simplifying a polynomial requires that you combine all
- For polynomials with only one variable, like
terms means that the power of the variable
is the same. For example, 3x 5 and -2x 5
are like terms, but 2a 4 and 2a 2
- You CANNOT combine terms that are not
like. For example, there is no way to add x
3 and x 2. ( x 3 + x 2
x 5 = x 2 x 3
- Keep in mind that the variable in a polynomial represents
a number. Every time a variable appears, it represents
the SAME number. For example, if x = 2, then the
polynomial x 3 - 5x 2 + x - 5 is
the same as 2 3 - 5(2 2) + 2 - 5 =
8 - 20 + 2 - 5 = -15.