Polynomials (Section 1-4) Introduction Operations.

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Presentation transcript:

Polynomials (Section 1-4) *Introduction *Operations

Polynomial: What is it? These are: ■ These are NOT:

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 3x 2 y 5 z has 1 term 3x 2 +y 5 z has 2 terms 3–x 2 +y 5 z has 3 terms

Terms of Polynomials 1monomial3x 2 y 5 2binomial3x 2 +y 5 3trinomial3–x 2 +y 5 4+no special name 3x 5 –2x 4 +5x 3 –6x 2 +2x

Vocabulary of Monomial 3x 2 3 is the numerical coefficient x is the base 2 is the exponent x 2 is a power (the second power of x)

Find degrees of polynomials 5 th degree 3 rd 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 DegreeNameExample 0Constant13 1 st Linear5x 2 nd Quadratic7x 2 3 rd Cubic5x 3 4 th Quarticx4x4 5 th Quintic9x 5 6 th +No special name3x 17

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 + 3d 2 = 5d + 3d 2

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 + 2cd 2 = 5cd + 2cd 2

Multiplying Polynomials