UNIT 2, LESSON 1 POLYNOMIAL FUNCTIONS. WHAT IS A POLYNOMIAL FUNCTION? Coefficients must be real numbers. Exponents must be whole numbers.

UNIT 2, LESSON 1

POLYNOMIAL FUNCTIONS

WHAT IS A POLYNOMIAL FUNCTION?

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21

1 ... axaxaxaxaxP nn

nn

nn

• Coefficients must be real numbers.• Exponents must be whole numbers.

COMPONENTS

• Leading Coefficient• Leading Term• Degree• Constant Term

012

21

1 ... axaxaxaxaxP nn

nn

nn

COMPONENTS

• Leading Coefficient• Leading Term• Degree• Constant Term

012

21

1 ... axaxaxaxaxP nn

nn

nn

COMPONENTS

• Leading Coefficient• Leading Term• Degree• Constant Term

012

21

1 ... axaxaxaxaxP nn

nn

nn

COMPONENTS

• Leading Coefficient• Leading Term• Degree• Constant Term

012

21

1 ... axaxaxaxaxP nn

nn

nn

COMPONENTS

• Leading Coefficient• Leading Term• Degree• Constant Term

012

21

1 ... axaxaxaxaxP nn

nn

nn

SPECIAL FUNCTIONS

•Constant•Linear•Quadratic•Cubic•Quartic

END BEHAVIOR

END BEHAVIORLead CoefficientPositive

Degree = Even

Lead CoefficientNegative

Degree = Even

END BEHAVIORLead CoefficientPositive

Degree = Even

Lead CoefficientNegative

Degree = Even

Lead CoefficientPositive

Degree = Odd

Lead CoefficientNegative

Degree = Odd

MULTIPLICITY OF ROOTS

• If r is a zero of a polynomial and the exponent on the term that produced the root is k then we say that r has multiplicity k.• For example, the polynomial

will have one zero, x=5, and its multiplicity will be 2

http://tutorial.math.lamar.edu/Classes/Alg/ZeroesOfPolynomials.aspx

LIST THE MULTIPLICITIES OF THE ZEROES OF EACH OF THE FOLLOWING

POLYNOMIALS.

1.

2.

3.

http://tutorial.math.lamar.edu/Classes/Alg/ZeroesOfPolynomials.aspx