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

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.

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

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

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

MODEL #1 2 𝑥 3 + 𝑥 2 −5𝑥+12

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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