1. 5-3 Dividing Polynomials Objectives Students will be able to: 1) Divide polynomials using long division 2) Divide polynomials using synthetic division

2. Example 1: Polynomial/Monomial

3. Ex 1B: Polynomial/Monomial Simplify.

4. Ex 1C: Polynomial/Monomial Simplify.

5. Apply Concepts1: Simplify! 1.2.

6. Remember Long Division?

7. Polynomial Long Division 1) Rewrite the problem in long division form (if not already done). 2) In each polynomial, line the terms up in descending order, with respect to their degree. 3) Within the numerator (dividend), if a degree term is missing, add it in with a 0 coefficient. Example: is missing the second degree term, so add it in.

8. Ex 2:Division Algorithm 6(z – 4) = 6z – 24

9. Ex 2B: Division

10. Ex 2C: Division

11. Ex 2D: Division

12. Ex 3: Quotient With Remainders Simplify:

13. Ex 3B: Remainders

14. Ex 3C: Remainders

15. Synthetic Division Synthetic division: method of polynomial long division using only the coefficients of the terms In order to use synthetic division, the denominator (divisor) must be a first degree binomial, which takes on the form Also, the coefficient on the first degree term of the divisor must be a 1. Let’s examine the steps of synthetic division while working through a problem.

16. Synthetic Division

18. Ex 4:Synthetic Division

19. Ex 4B: Synthetic Division