1. Warm - Up
Divide using long division
150 / 7 7

2. Announcements Assignment p. 239 # 1, 7, 8 - 20 even
2.1 – 2.3 Quiz Friday
Please pass up last night’s homework

3. 2.3 Polynomial and Synthetic Division
Kenwood Students will be able to:
use long division to divide polynomials by other polynomials
use synthetic division to divide polynomials by binomials of the form (x  k)

4. Why spend our time on it?
If we are given one x-intercept, we can find the others using division

5. Long Division to divide polynomials by other polynomials

6. Procedure Divide first terms Multiply times the divisor
Subtract by changing the signs and adding
Bring down the next term and begin the process again

7. 1.Divide first terms
Try to make the first terms equivalent so they will cancel 2x

8. 2.Multiply times the divisor2x

9. 3. Subtract by changing the signs and adding2x 4x

10. 4. Bring down the next term and begin the process again

11. Result???
=2x + 4 2x +4

12. Example 1. Divide 2x3 – 5x2 + x – 8 by x – 3.
Quotient
Dividend
Divisor
Remainder

13. Division Algorithm How do we write our answer?
 f(x) = function
 d(x) =Divisor
 q(x) = quotient
 r(x) = remainder
Please go back to the first example and label f(x), d(x), q(x) and r(x) in the first problem

14. Example 2. Please find the values of a, b, c

15. Example 3. Divide 5x2 – 17x - 12 by x – 4.
Please complete this question on a separate sheet of paper to be turned in.

16. Warm – Up from the assignment
16)
18)
20)

17. Announcements 2.1 – 2.3 Quiz Friday Assignment p. 239
# 23, 24 – 32 even, 49
2.1 – 2.3 Quiz Friday

18. Synthetic Division

19. Procedure Find “a”, what x equals
Write the coefficients and “a” in the synthetic division format
Bring down the first coefficient. Then multiply and add for each column.
Write the quotient

20. Example # 1

21. Step 1
Find “a”, what x equals
(x – 2) = 0
X = 2

22. Step 2
Write the coefficients and “a” in the synthetic division format
Drop down the coefficients into a line 2

23. Step 3
Bring done the first coefficient. Then multiply and add for each column. 2

24. Step 4
Write the quotient 2

25. Comparing Long Division and Synthetic Division
Purpose
Use when you have a division problem involving two polynomials.
Used only in the case of division by a linear factor
Advantage
Will work for any division problem
Shorter process
Disadvantage
Longer work process
Longer Set - Up
Set - Up
Set up exactly like an integer division problem
Only the coefficients of the polynomial are used

26. Example 2. Divide 3x3 – x2 + 5x – 3 by x – 2.
How is Synthetic Division connected to Long Division? -2 3 -1 2 -3
( - ) -6
-10
-24 5 12 21

27. Example #3
What to we have to do to keep the place holders?

28. Example # 2

29. Procedure – Step 1
Find “a”, what x equals
(x – 3) = 0
X = 3

30. Step 2
Write the coefficients and “a” in the synthetic division format 3

31. Step 3
Bring done the first coefficient. Then multiply and add for each column. 3

32. Step 4
Write the quotient 3

33. Warm - Up
1) 2)

34. Announcements Assignment 2.1 – 2.3 Quiz tomorrow p. 239
# 11, 17, 23, 27, 45, 47
Review notes from 2.1 and 2.2
2.1 – 2.3 Quiz tomorrow

35. Factor Theorem
If a number (k) is a factor, then there will be no remainder.
How could we test for that?
Substitute the value into the function and find out if there is a remainder
Are 1, 2, 0, -1 factors of f(x) = x4 – 1?

36. Remainder Theorem
The remainder for any division problem for a number (k) will be f(k)
What is the remainder if x = 1?

37. Things to know for the 2.1 – 2.3 Quiz
How to use long division to solve
How to use synthetic division to solve
Find the equation of a quadratic function given the vertex and a point
Find the vertex given an equation
Find the real zeros of a polynomial
How to use the factor theorem
How to use the remainder theorem

38. Cooperative Assignment
Please sit quietly in groups of four (4).
On your own sheet of paper, work on one of the 4 questions alone for 3 minutes.
When time is up, pass your question slips to your left to the next person in the group.
Continue step 3 until all 4 group members have completed each question.
Next, you will share your answers with the other students in their groups, one question at a time. The group should come to an agreement about the correct answer to the question.
When you have agreed on an answer to a question, put the work on a post-it with the following info: question #, group name, agreed-upon answer to the question. Do this for all four questions.
Have one person from your group put the 4 questions on the board.