1. Objective Please copy on your packet
Students will perform polynomial operations to be able to provide an equivalent form of the polynomial.

2. QUICK Review
Looking at your objective, what words stand out and do you know what they mean?
Rewrite in an equivalent form: 5𝑎+3𝑏−2𝑎+7𝑏
Rewrite in an Equivalent form: 3(𝑥−7)
Provide one at a time the following problems to students. Have the conversation about the step needed in order to complete the rewrite in the equivalent form asked. In this case students are simplify the provided expression. Students should not only write their responses to the questions on the slide, but should note the operations in which they had to perform to get them to their final result.

3. exponent monomial Vocabulary
A ___________________ is a number, a variable, or the product of a number and one or more variable with whole number ____________________.
exponent

4. term polynomial Vocabulary
A _______________ is a monomial or a sum or monomials, each called_________ of the polynomial.
term

5. variable decrease left right Leading coefficient polynomial Vocabulary
When a _____________ is written so that exponents of a __________ _____________ from ________ to ___________ the coefficient of the first term is called the _________________________________
variable
decrease
left
right
Leading coefficient

6. MODEL #1
2 𝑥 3 + 𝑥 2 −5𝑥+12

7. degree
The _______________ is also the maximum of potential zeros of a polynomial function.

8. Today’s Activity
On the next few slides are going to be some examples of polynomials that need to be rewritten in an equivalent form.
Once the problem appears on the board you will be responsible (Individually) to provide an equivalent form on your white boards. (Approx. 90 seconds)
Then you will share your response with the person you are sitting next to. Compare your answers. Determine which answer you like the best and determine why. (Approx. 90 Seconds)
And be ready explain your answer to the class.

9. Examples Menu Example 1- Adding Polynomials
Example 2 – Subtracting Polynomials
Example 3- Multiplying Polynomials A B C D
Not all problems need to be complete.
Modeling a problem prior to the students attempting on their own is a reasonable expectation.
PARCC RELATED

10. Adding Polynomial Example 1 A
2 𝑥 3 −5 𝑥 2 +𝑥 +(2 𝑥 2 + 𝑥 3 −1)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

11. Adding Polynomial Example 1 B
3 𝑥 2 +𝑥−6 +( 𝑥 2 +4𝑥+10)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

12. Adding Polynomial Example 1 C
−2 𝑥 2 +3𝑥− 𝑥 3 +(3 𝑥 2 + 𝑥 3 −12)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

13. Adding Polynomial Example 1 D
4 𝑥 3 +2 𝑥 2 −4 +(−3𝑥+ 𝑥 3 +𝑥)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

14. Subtracting Polynomial Example 1 A
4 𝑛 2 +5 −(−2 𝑛 2 +2𝑛−4)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

15. Subtracting Polynomial Example 1 B
4 𝑥 2 −𝑥+5 −(3 𝑥 2 −𝑥−8)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

16. Subtracting Polynomial Example 1 C
2 𝑐 2 −8 −(3 𝑐 2 −4𝑐+1)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

17. Subtracting Polynomial Example 1 D
5 𝑦 2 +2𝑦−4 −(− 𝑦 2 +4𝑦−3)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

18. Multiplying Polynomial Example 1 A
𝑥(7 𝑥 2 +4)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

19. Multiplying Polynomial Example 1 B
(𝑎+3)(2𝑎+1)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

20. Multiplying Polynomial Example 1 C
(4𝑛−1)(𝑛+5)
0:28
0:29
0:31
0:27
0:30
0:25
0:22
0:23
0:24
0:32
0:26
0:34
0:39
0:40
0:41
0:42
0:38
0:37
0:21
0:35
0:36
0:33
0:19
0:05
0:06
0:07
0:08
0:04
0:03
1:30
End
0:01
0:02
0:09
0:10
0:16
0:17
0:18
1:30
0:15
0:14
0:11
0:12
0:13
0:20
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
0:44
1:07
0:51
0:52
0:53
0:54
0:50
0:49
0:45
0:46
0:47
0:48
1:06
0:55
1:02
1:03
1:04
1:05
0:56
1:01
0:57
1:00
0:58
0:59
Menu

21. Multiplying Polynomial Example 1 D
(𝑥+4)(2𝑥−1)
Ask student to complete this as the exit ticket and submit prior to the end of the class period.
Assign homework based on today’s instruction.
0:27
0:28
0:30
0:26
0:29
0:23
0:21
0:22
0:31
0:24
0:25
0:33
0:38
0:39
0:40
0:41
0:37
0:36
0:20
0:34
0:35
0:32
0:18
0:04
0:05
0:06
0:07
0:03
0:02
1:30
End
0:01
0:08
0:09
0:15
0:16
0:17
0:42
0:14
0:13
0:10
0:11
0:12
0:19
0:43
1:14
1:15
1:16
1:17
1:13
1:12
1:08
1:09
1:10
1:11
1:18
1:19
1:26
1:27
1:28
1:29
1:25
1:24
1:20
1:21
1:22
1:23
1:07
1:06
0:50
0:51
0:52
0:53
0:49
0:48
0:44
0:45
0:46
0:47
0:54
0:55
1:02
1:03
1:04
1:05
1:01
1:00
0:56
0:57
0:58
0:59
1:30
Menu

22. PARCC Related Question (Sample Problem)
Rewrite the expression
−3𝑎 𝑎+𝑏−5 +4 −2𝑎+2𝑏 +𝑏 𝑎+3𝑏−7
to find the coefficients of each term. Fill in the coefficients on the appropriate lines below.
_______ 𝑎 2 +_______ 𝑏 2 +______𝑎𝑏+_______𝑎+_______𝑏