Polynomials are algebraic expressions made up of terms that are added, subtracted, or multiplied, where each term involves variables raised to non-negative integer powers. Polynomials can be composed of constants, single variables, or multiple variables with positive exponents, and adding or multiplying polynomials results in another polynomial. Standard form for polynomials lists terms in descending order of variable exponents from highest to lowest.

1. POLYNOMIALS

2. Polynomial

An expression of finite length

Finite= has limit; definite; countable;
measurable

made up of terms that are only added,
subtracted or multiplied

comes form poly- (meaning "many") and
-nomial (in this case meaning "term") ... so it
says "many terms"

3. Composition of Polynomials

Constants

Variables

Variables with positive exponents

can have no variable at all

Can have one variable

4. What's special about
polynomials?

If you add polynomials you get a polynomial

If you multiply polynomials you get a polynomial

5. Standard form

Those variables with highest exponents go first

Descending order of exponents
4 2
x −2x + x

6. Example Graph of a Polynomial

Example: x 4−2x 2+ x

7. Examples: Polynomials?
x√ 4
3
4x+2x
2x
3x 3 +0.0001
5y− s
3
x
2

8. POLYNOMIALS?
2
1. √ x 2. 23x
[ x−1]
2 −1
3. 23x 4. y
√x 2
5. −1
( )
2
z

9. Monomials, Binomials, Trinomials

Basically, these are polynomials

Monomials are one-term polynomials
2 3
ex. 3x, 3x y

Binomials are... guess what...
two-term polynomials
4 4
ex. 10x-3 , 4x −5y

Trinomials?
Polynomials with three terms
2
ex. 2x +3y+1

11. DISCIPLES OF CONFUSIONISM?

12.  QUESTIONS
 CLARIFICATIONS?
 VIOLENT
REACTIONS?

13. SOURCE WEBSITE
http://www.mathsisfun.com/algebra/polynomials.html