1. Write a letter to Janet explaining her error and then correctly solve the problem below. You may NOT use your notes or talk with your partner. Add(3x 3 + 5x 2 – 7x + 2) + (6x 3 - 8x 2 + 2x – 5) 3x 3 + 5x 2 – 7x2 6x 3 18x 6 30x 5 - 42x 4 12x 3 - 8x 2 -24x 5 -40x 4 56x 3 - 16x 2 + 2x6x 4 10x 3 -14x 2 4x – 5- 15x 3 -25x 2 35x-10 Janet’s answer 18x 6 +6x 5 -76x 4 +63x 3 – 55x 2 +39x – 10

2. Objective: Students will be able to demonstrate their understanding of factoring when a ≠1 by 1) correctly solving at least 2 of the 4 “you try” problems, 2) completing at least 1 problem via AB partner teach, and 3) scoring at least a 2 on their exit slip.

3. Standard 11.0 Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials..

4. FACTORING WHEN A ≠ 1 RULES 1. Multiply a & c and list the pairs of numbers that multiply to equal the value of (a)(c) 2. From those factors, pick a pair that either add or subtract to get b. 3. Write the temporary factors with the two numbers. 4. Put the value of a under both of your temporary factors. 5. Reduce the fractions, if possible. 6. Move denominators in front of x and list the factors.

5. Factor 2x 2 – 5x – 7

6. Factor 15x 2 + 7x – 2

7. Subtracting Polynomials Factor 1. 3x 2 + 14x + 8 2. 10x 2 – 23x + 12 1. 3x 2 + 26x + 35 2. 2x 2 + 7x + 6

8. 1. Based on the problems we’ve just done, list the steps (without looking at your notes) to factoring when a ≠ 1 so that your partner can do a problem using only your steps. 2. Trade papers with your partner and use their steps to factor the following problem: 4x 2 + 4x – 3 3. If you cannot complete the problem using only the steps written, put an arrow on the step where you stopped. 4. Give your partner’s paper back to them. Modify the steps you wrote to correct any incomplete or incorrect steps. 5. Finish the problem based on your partner’s new steps. 6. Try using the steps again to factor: 3x 2 + 11x – 20

9. Subtracting Polynomials Factor 1. 2x 2 - 7x + 3 2. 3x 2 + 2x - 5 1. 4x 2 + 12x + 5 2. 2x 2 + 3x + 1