1. Warm-up

2. Warm-up Answers

3. Dividing Polynomials: Objectives: ◦Determine the best method to factor rational expressions. ◦Divide rational expressions using long division and synthetic division. ◦Apply the methods to real-life situations.

4. Why is this important??? You can use polynomials to solve problems involving manufacturing and entertainment

5. Application Joy, a senior at Burlington Township HS, spends one free period a day as a TA at the middle school located next to the high school. A magician was performing at the middle school and asked a member of the audience to participate in a number game.

6. Application continued The magician said: choose any number Multiply the number by 3 Add the sum of your number and 8 to the number you got when you multiplied. now divide by the sum of your number and 2

7. Dividing Polynomials Polynomial by a Monomial

8. Dividing Polynomials Polynomial by a Monomial

9. Dividing Polynomials Polynomial by a Monomial

10. Divide using long division

11. Dividing Polynomials using LONG DIVISION Polynomial by a Binomial

12. Dividing Polynomials using LONG DIVISION Polynomial by a Binomial

13. Dividing Polynomials using LONG DIVISION Polynomial by a Binomial

14. Dividing Polynomials Note: The leading coefficient of the divisor is not 1.

15. Dividing Polynomials NOTE: Polynomial with Missing Terms

16. Dividing Polynomials Polynomial with Missing Terms and/or divisor with a leading coefficient not equal to 1.

17. … using Synthetic Division

20. Synthetic Division 1.Put the polynomial in the dividend in descending order. 2.Determine if the dividend has missing terms. –If there are any missing terms, hold their space with a zero. –Write the coefficients and constant in a row. 3.Solve the divisor for 0. 4.Drop the first number down. ◦Multiply this number by the number in the box. ◦Add down. ◦Multiply this number by the number in the box. ◦Add down. ◦Continue this pattern. (x 3 + 2x – 5) (x – 2) 2 1 0 2 -5 2 4 12 1 2 6 7 x 2 x # R Solution: x 2 + 2x + 6 +

21. Class work ◦Sage and Scribe

22. TOTD 1. Illustrate why it is necessary to include terms with zero coefficients in the row of numbers for synthetic division. 2. Compare long division to synthetic division. Are there any advantages to either method? Which do you prefer? Why?

23. Homework ◦Worksheet, do it the exact same way we did the examples in class.

24. Warm - up