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Section 5.5: Apply the Remainder and Factor Theorems

Section 5.5: Apply the Remainder and Factor Theorems. Objective: By following instructions, students will be able to: use theorems to factor polynomials. example 1. Divide by. example 2. Divide using long division. Divide by . Your-Turn #1.

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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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