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Classifying Polynomials

Classifying Polynomials. Polynomial Terms. Polynomial – A monomial or sum of monomials. Polynomial Function – A function in the form of: + Where n = degree. Polynomial Terms. • Standard Form of a Polynomial – a polynomial whose terms are written in descending order.

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Classifying Polynomials

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  1. Classifying Polynomials

  2. Polynomial Terms • Polynomial – A monomial or sum of monomials. • Polynomial Function – A function in the form of: • + • Where • n = degree

  3. Polynomial Terms • Standard Form of a Polynomial – a polynomial whose terms are written in descending order. • Degree of a Polynomial- the highest exponent in any term of a polynomial

  4. Polynomials

  5. Steps to Using the ti 84 calculator • We have talked in the past about modeling data with lines and parabolas. Sometimes a polynomial of degree 3 or higher fit the data better. A graphing calculator can be used to find these equations. 1. Enter data in Lists (STAT enter) STAT → CALC ↓ 4: LinReg (ax + b) 5. QuadReg 6. CubicReg (You could also turn on STAT PLOT to view the points!)

  6. End Behavior of a Graph x → ∞ f(x) → ∞ x → ∞ f(x) → ∞ x → -∞ f(x) → -∞ Odd x → -∞ f(x) → ∞ Even Even x → -∞ f(x) → ∞ Odd x → -∞ f(x) → -∞ x → ∞ f(x) → -∞ x → -∞ f(x) → -∞ Identify its end behavior:

  7. End Behavior of a Graph 1. 2. Even Odd 4. 3. Odd Even Its end behavior identifies whether a polynomial is an even or odd function.

  8. Identify End Behavior of a polynomial Equation Odd Even

  9. Identify End Behavior of a polynomial Equation Odd Even What does even/odd function tell you?

  10. Add and subtract polynomials • To add or subtract polynomials, write in descending order, then combine like terms. You can add or subtract horizontally or vertically.

  11. practice • B. A.

  12. Your turn • B. A.

  13. Multiplying polynomials

  14. Multiplying polynomials

  15. Special product patterns (page 347) • Sum and Difference • (a + b)(a – b) = Square of binomial • = a2 + 2ab + b2 • = a2– 2ab + b2 Cube of a binomial • 3 + 3a2b + 3ab2 + b3 • 3– 3a2b + 3ab2– b3

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