Polynomials

Nomial is another name for number or term. Poly means many. A polynomial is many numbers or many terms.

In algebra 1 we work with:

Monomials - - which means one term

Examples:

5
x
12y
-8xyz

Binomials - - which means two terms

Examples:

2x - 6
x + y
-8xyz + 12x

Notice that binomials are in lowest terms and have no like terms that can be combined.


Trinomials - - which means three terms

Examples:















Each of these polynomials also has a DEGREE (or power). We find the degree by finding the highest power of each term. The term with the highest power sets the degree for the polynomial.


Polynomials can be:
constant
(0 degree)

linear
(1st degree)

quadratic
(2nd degree)

cubic (3rd degree)

4th degree

5th degree

and on and on.






However, the highest degree of a polynomial is the combination of the powers in each individual term.








Standard Form of a Polynomial

As we have learned this year, there are specific ways to write algebraic terms. When writing polynomials we write them from the highest exponent to the lowest exponent.




They are also written in reduced form so all mathematical process that can be done, must be done and all like-terms must be combined so the polynomial is in standard form.


Your final answer must be written in standard form, in lowest term.




Adding Polynomials



Adding vertically may be the easiest procedure:












Remember to line up like terms so you are combining like variable with the same exponent.










Subtracting Polynomials


You must remember to distrbute the negative sign into the parentheses.