Polynomials (Section 1-4)

*Introduction

*Operations

Polynomial: What is it?

These are: ■ These are NOT:

x

x

xyx

x

2

2

1975

22

x

x

x

xyx

x

2

2

2

1975

21

Polynomial: What is it?

These are: ■ These are NOT:

Only operations Has any other

on the variable operation on

are +, -, x the variable

Terms in an Expression

Number of items added or subtracted

3x2y5z has 1 term

3x2+y5z has 2 terms

3–x2+y5z has 3 terms

Terms of Polynomials 1 monomial 3x2y5

2 binomial 3x2+y5

3 trinomial 3–x2+y5

4+ no special name3x5–2x4+5x3–6x2+2x

Vocabulary of Monomial

3x2

3 is the numerical coefficient

x is the base

2 is the exponent

x2 is a power (the second power of x)

Find degrees of polynomials

32

324

4

32

5

5

yx

yx

xy

yx

x

5th degree

5th degree

5th degree

5th degree

3rd degree

Definition of Degree

The degree of a polynomial is the maximum number of variables that appear as factors in any one term.

Vocabulary of Degrees

Degree Name Example

0 Constant 13

1st Linear 5x

2nd Quadratic 7x2

3rd Cubic 5x3

4th Quartic x4

5th Quintic 9x5

6th + No special name 3x17

Adding or Subtracting Terms

2 alligators + 3 alligators =

5 alligators

2a + 3a = 5a

Adding or Subtracting Terms

2 alligators + 3 beavers =

2 alligators + 3 beavers

2a + 3b = 2a + 3b

Adding or Subtracting Terms

5 ducks + 3 two-headed ducks =

5 ducks + 3 two-headed ducks

5d + 3d2 = 5d + 3d2

Adding or Subtracting Terms

5 CoyoteDucks + 2 CoyoteDucks =

7 CoyoteDucks

5cd + 2cd = 7cd

Adding or Subtracting Terms

5 CoyoteDucks + 2 Ducks =

5 CoyoteDucks + 2 Ducks

5cd + 2d = 5cd + 2d

Adding or Subtracting Terms

5 CubDucks + 2 CubTwo-headedDucks =

5 CubDucks + 2 CubTwo-headedDucks

5cd + 2cd2 = 5cd + 2cd2

Multiplying Polynomials

32

235

35

35

35

ba

ba

bab

aa

a

Multiplying Polynomials

62332

1015235

1535

1535

1535

2

2

baabba

baba

abbab

aaa

aa