1. Synthetic Division 29 October 2010

2. Operations on Polynomials Recap – We know how to: Add Subtract Multiply What about division?

3. Dividing Polynomials Like long division We have a short cut! Synthetic Division!!!

4. Dividing Polynomials Synthetic Division Only works when we divide by 1 st degree (linear) polynomials My degree can’t be larger than 1!

5. Synthetic Division

6. Your Turn On the “Synthetic Division” handout, complete problems 1 – 5. You will: Decide if it’s possible to use synthetic division to divide the two polynomials

7. Division Vocab Review DividendDivisorQuotient

8. Preparing for Synthetic Division Can only be used when the divisor is in the form x – c If the divisor isn’t in the form x – c, then you need to convert the expression to include subtraction.

9. Preparing for Synthetic Division, cont.

10. Polynomials need to be written in expanded, standard polynomial form. Translation: If you’re missing terms, then you need to write them out as 0 times (*) the appropriate term.

11. Preparing for Synthetic Division, cont.

12. Your Turn On “Synthetic Division” handout, write the dividend in expanded standard polynomial form for problems 6 – 10. Write the divisor in the form x – c.

13. *Synthetic Division Steps Example Problem:

14. Prep Step Divisor x – c? x – 2 Dividend in Expanded Standard Polynomial Form? 3x 4 – 8x 2 – 11x + 1 3x 4 + – 8x 2 – 11x + 1 3x 4 + 0x 3 – 8x 2 – 11x + 1

15. Step 1 2 Write the constant value of the divisor (c) here.

16. Step 2 2 Write all the coefficients of the expanded dividend here. 3 0 -8 -11 1

17. Step 3 2 “Drop” the 1 st coefficient underneath the line. 3 0 -8 -11 1 3

18. Step 4 2 Multiply “c” by the last value underneath the line. Write their product just underneath the next coefficient. 3 0 -8 -11 1 6 3

19. Step 5 2 Add together the numbers in that column and write their sum underneath the line. 3 0 -8 -11 1 6 3 6

20. Step 6 2 Multiply “c” by the last value underneath the line. Write their product just underneath the next coefficient. 3 0 -8 -11 1 6 12 3 6

21. Step 7 2 Repeat steps 5 and 6 until a number appears in the box underneath the last column. 3 0 -8 -11 1 6 12 8 -6 3 6 4 -3 -5

22. Step 8 – Naming the Quotient 2 In the last row are the coefficients of the quotient in decreasing order. The quotient is one degree less than the dividend. 3 0 -8 -11 1 6 12 8 -6 3 6 4 -3 -5

23. Step 8 – Naming the Quotient 3 6 4 -3 -5 The number in the box is the remainder. 3x 3 + 6x 2 + 4x – 3 Remainder -5

24. Your Turn On the “Synthetic Division” handout, solve for the quotient of problems 11 – 14 using synthetic division. You may work with your partner.