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Section 5.5: Apply the Remainder and Factor Theorems

Learn to apply the Remainder and Factor Theorems for polynomial factorization. Examples of division, synthetic division, and factoring. Identify zeros and model profit functions. Practice questions included.

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Section 5.5: Apply the Remainder and Factor Theorems

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  1. Section 5.5: Apply the Remainder and Factor Theorems

  2. Objective: By following instructions, students will be able to: • use theorems to factor polynomials.

  3. example 1 Divide by .

  4. example 2 Divide using long division. Divide by .

  5. Your-Turn #1 Divide using polynomial long division. a) b)

  6. example 3 Divide by using synthetic division.

  7. Theorem A polynomial f(x) has a factor of x-k if and only if f(k)=0.

  8. example 4 Factor a polynomial. Factor completely given that is a factor.

  9. Your-Turn #2 • Divide using synthetic division. • b) Factor given that is a factor.

  10. example 5 Factor a polynomial. One zero of is . What is another zero of the function?

  11. example 6 Use a polynomial model The profit P (in millions of dollars) for a shoe manufacturer can be modeled bywhere x is the number of shoes produced (in millions). The company now produces 1 million shoes and makes a profit of $25,000,000, but would like to cut back production. What lesser number of shoes could the company produce and still make the same profit?

  12. Your-Turn #3 • Find the other zeros of given that .

  13. Revisit Objective: Did we… • use theorems to factor polynomials?

  14. HW: Sec 5.5 pg 366 #s 3-33 ODD, 36

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