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Polynomials

Polynomials. Polynomials. Types of Polynomials About Polynomials Graphing Polynomials Evaluating Polynomials. Types of Polynomials. Monomial Binomial Trinomial Polynomial. Types of Polynomials.

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Polynomials

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  1. Polynomials

  2. Polynomials • Types of Polynomials • About Polynomials • Graphing Polynomials • Evaluating Polynomials

  3. Types of Polynomials • Monomial • Binomial • Trinomial • Polynomial

  4. Types of Polynomials A polynomial is a broad term for a function that only has many terms with positive integer exponents. is not a polynomial.

  5. About Polynomials • Standard form of a polynomial is when the terms of a polynomial are written in descending order of exponents. is not in standard form. is in standard form.

  6. Rewrite the Polynomials in Standard Form

  7. About Polynomials • The leading coefficient is number of the term with the highest degree.

  8. Identify the Leading Coefficient

  9. About Polynomials • The degree of the polynomial is the the greatest exponent.

  10. Identify the Degree of the Polynomial

  11. y 10 10 8 6 4 2 x -10 -10 -8 -6 -4 -2 2 4 6 8 10 10 -2 -4 -6 -8 -10 -10 Graphs of Polynomials

  12. y y 10 10 8 8 6 6 4 4 2 2 x x -10 -10 -10 -10 -8 -8 -6 -6 -4 -4 -2 -2 2 2 4 4 6 6 8 8 10 10 -2 -2 -4 -4 -6 -6 -8 -8 -10 -10 -10 -10 Even Exponents • Positive Leading Coefficient • Negative Leading Coefficient

  13. y y 10 10 8 8 6 6 4 4 2 2 x x -10 -10 -10 -10 -8 -8 -6 -6 -4 -4 -2 -2 2 2 4 4 6 6 8 8 10 10 -2 -2 -4 -4 -6 -6 -8 -8 -10 -10 -10 -10 Odd Exponents • Positive Leading Coefficient • Negative Leading Coefficient

  14. Graph on your Calculator

  15. Evaluating Polynomials Using Synthetic Substitution

  16. Why not just “plug it in?” • Don’t really need a calculator. • We’ll use the idea to make dividing polynomials, which can be difficult, an easier task.

  17. 1. Rewrite the coefficients and put the “2” we’re evaluating to the side. 2 -3 -4 8 2|

  18. 2. Bring down the “2”. 2 -3 -4 8 2| 2

  19. 3. Multiply the “2” on the side by the “2” that was brought down and put product below “-3”. 2 -3 -4 8 2| 4 2 x =

  20. 4. Add -3 and 4 and write sum below. 2 -3 -4 8 2| +4 2 1

  21. 5. Multiply the “2” on the side by the “1” that was brought down and put product below “-4”. 2 -3 -4 8 2| +4 2 2 1 x =

  22. 6. Add -4 and 2 and write sum below. 2 -3 -4 8 2| 4 +2 2 1 -2

  23. 7. Multiply the “2” on the side by the “-2” that was brought down and put product below “8”. 2 -3 -4 8 2| 4 +2 -4 2 1 -2 x =

  24. 8. Add 8 and -4 and write sum below. 2 -3 -4 8 2| 4 +2 -4 2 1 -2 4

  25. You try one!

  26. Try a Tricky One!

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