Division of Polynomials Using 2 Long Division and Synthetic Division Method

A powerpoint presentation that focuses on the division of polynomials

1. Module 7: Division of Polynomials Mathematics 10

2. Drill

3. A. Divide the ff. 1.   2.   3.   4.  

4. B. Multiply the ff. 1.   2.   3.   4.  

5. Review

6. Polynomials A polynomial expression P(x) is an expression of the form   Where: and the degree n is a non-negative integer . The coefficients are real numbers.  

7. Polynomials Writing the terms in decreasing powers of the variable x is said to be in Standard Form . By Convention:

8. Which is not a polynomial?    

9. Which is not a polynomial?    

10. Which is not a polynomial?    

11. Which is not a polynomial?    

12. Which is not a polynomial?    

13. Division of Polynomials

14. Division Statement         Since the remainder is 0, 6 is a factor of 24.

15. Division Statement         Since the remainder is not equal to 0, 6 is not a factor of 29.

16. Division of Polynomials   Multiply both sides by D(x).   If P(x) and D(x) are polynomials, then

17. The R(x) is either zero or its degree is less than the degree of D(x). If R(x) = 0, then D(x) is a factor of P(x).

18. Long Division

19. Divide the following polynomials using long division: 1. (7x 3 + 16x 2 + 2x – 1) (x + 4)   REMEMBER! Always arrange both the P(x) and D(x) in the descending powers of the variable x.    

21.     OR P(x) = D(x) Q(x) + R(x)    

22. Divide the following polynomials using long division: 2. (27x 3 + 8) (3x + 2)      

24.     OR P(x) = D(x) Q(x) + R(x)    

25. Divide the following polynomials using long division: 3. (5x 4 – 3x 2 + 2x - 6) (x 2 - 2x + 3)      

27.     OR P(x) = D(x) Q(x) + R(x)    

28. Synthetic Division

29. When a polynomial is to be divided by a binomial of the form x – c , we can shorten the process by using Synthetic Division.

30. Divide the following polynomials using synthetic division: 1. (3x 3 – 10x 2 – 9x + 15) (x – 4)    

31. Procedures: (3) (4) = 12 -10 + 12 = 2 (2) (4) = 8 -9 + 8 = -1 (-1) (4) = -4 15 + (-4) = 11 3 -10 -9 15 12 8 -4 3 2 -1 11 Numerical coefficients of P(x) in Standard Form. 4 Quotient:  

32. Divide the following polynomials using synthetic division: 2. (x 3 + 6x 2 – x - 30) (x – 2)    

33. Procedures: (1) (2) = 2 6 + 2 = 8 (8) (2) = 16 -1+ 16 = 15 (15) (2) = 30 -30+ 30 = 0 1 6 -1 -30 2 16 30 1 8 15 0 Numerical coefficients of P(x) in Standard Form. 2 Quotient:  

34. Divide the following polynomials using synthetic division:   3. (3x 3 – 7x 2 – 20) (x – 3)  

35. Procedures: (3) (3) = 9 -7 + 9 = 2 (2) (3) = 6 0 + 6 = 6 (6) (3) = 18 -20 + 18= -2 3 -7 0 -20 9 6 18 3 2 6 -2 Numerical coefficients of P(x) in Standard Form. 3 Quotient: