1. LESSON 3: THE DIVISION OF POLYNOMIALS A-SSE.A.2MP.7 A-APR.C.4MP.8 Opening Exercise 5 minutes, with explanation (2 slides)

2. OPENING EXERCISE - ANSWER

3. DISCUSSION (QUESTIONS FOR CONSIDERATION)

4. EXPLORATORY CHALLENGE STRUGGLE WITH THIS. WORK WITH IT UNTIL YOU CAN’T WORK ANY MORE, AND THEN WORK WITH IT SOME MORE. Going ahead prematurely will only hurt YOU.

5. PROMPTING QUESTIONS

6. SOLVING THE EXPLORATORY CHALLENGE Remember, during multiplication our FACTORS would go across the top and right sides. In division, one of the factors will be our divisor and the other one becomes our quotient. Setting up the larger expression as the dividend is the tricky part! Just work backwards. Remember that the results for what became our product (now the dividend) were the sum of all the cells in that diagonal.

7. SOLVING THE EXPLORATORY CHALLENGE Sample working through:

8. SOLVING THE EXPLORATORY CHALLENGE

11. One! Now as our last step, we rewrite the terms with their appropriate signs (in this case everything was positive, but there are times where we may have negative results along the top; keep the signs together).

12. EXERCISE 3

13. EXERCISE 3 (SOLUTION) Set up:Fill out the boxes you know:Use multiplication to discover the top:

14. ALRIGHT, THIS IS WEIRD…

15. SO HOW DO WE SET UP THE TABLE? Here’s the weird part (and you thought we already covered the weird, didn’t you?): The number of rows will be ONE MORE than the degree of the divisor. The number of columns will be ONE MORE than the difference of the degrees of the dividend and the divisor. At this point you can attempt the example, or move on to see the table.

16. EXAMPLE/EXERCISE 4

17. IN YOUR NOTES Please reflect, in your NOTE books, on the following questions. These will help drive our small group discussions: What strategies were helpful when you set up and solved these problems? What patterns did you notice as you solved these problems? What happens to the degree of the product when you multiply two polynomials? What happens to the degree of the quotient when you divide two polynomials? What happens to the leading coefficient when you multiply or divide polynomials? (We didn’t explicitly cover this one, but think about it in the context of your previous answers)