1. Module 7.15 Quanyka’s Quilts

2. 𝐴 𝑥 =(𝑥+5)(𝑥+2) 𝐴 𝑥 = 𝑥 2 +7𝑥+10 Add 5 inches on this side
Original Quilt
𝑥 2
Add 5 inches on this side
“Fill in the quilt”
Add 2 inches on this side
𝐴 𝑥 = 𝑥 2 +7𝑥+10

3. 𝐴 𝑥 =(𝑥+2)(𝑥+4) 𝐴 𝑥 = 𝑥 2 +6𝑥+8 Add 2 inches on this side
Original Quilt
𝑥 2
Add 2 inches on this side
“Fill in the quilt”
Add 4 inches on this side
𝐴 𝑥 = 𝑥 2 +6𝑥+8

4. 𝐴 𝑥 = 𝑥 2 +3𝑥 𝐴 𝑥 = 𝑥+0 𝑥+3 or 𝐴 𝑥 =𝑥(𝑥+3) Add nothing to this side
Original Quilt
𝑥 2
Add nothing to this side
Nothing to “fill in”
Add 3 inches on this side
𝐴 𝑥 = 𝑥 2 +3𝑥

5. 𝐴 𝑥 =(𝑥+6)(𝑥+6) 𝐴 𝑥 = 𝑥 2 +12𝑥+36 Add 6 inches to this side
Original Quilt
𝑥 2
Add 6 inches to this side
“Fill in the quilt”
Add 6 inches on this side
𝐴 𝑥 = 𝑥 2 +12𝑥+36

6. 𝐴 𝑥 =(𝑥+2)(𝑥+7) 𝐴 𝑥 = 𝑥 2 +9𝑥+14 Add 2 inches to this side
Original Quilt
𝑥 2
Add 2 inches to this side
“Fill in the quilt”
Add 7 inches on this side
𝐴 𝑥 = 𝑥 2 +9𝑥+14

7. Notice that this quilt had extensions of 3 inches and 6 inches…
𝐴 𝑥 = 𝑥 2 +3𝑥+6𝑥+18
There are 3 inches on this side
Original Quilt
𝑥 2
Notice that this quilt had extensions of 3 inches and 6 inches…
3 x 6 = 18
3 + 6 = 9
There are 6 inches on this side
𝐴 𝑥 = 𝑥 2 +9𝑥+18
𝐴 𝑥 =(𝑥+3)(𝑥+6)

8. 𝐴 𝑥 = 𝑥 2 +12𝑥+2𝑥+24 𝐴 𝑥 = 𝑥 2 +14𝑥+24 𝐴 𝑥 =(𝑥+12)(𝑥+2)
There are 12 inches on this side
Original Quilt
𝑥 2
Notice again…
12 x 2 = 24
= 14
There are 2 inches on this side
𝐴 𝑥 = 𝑥 2 +14𝑥+24
𝐴 𝑥 =(𝑥+12)(𝑥+2)

9. 8. 𝑥 2 +7𝑥+3𝑥+21
Factored form: (𝑥+7)(𝑥+3)
9. 𝑥 2 +3𝑥+𝑥+3
Factored form: (𝑥+3)(𝑥+1)

10. what can multiply to 9 and add up to 10??
10. 𝑥 2 +10𝑥+9
what can multiply to 9 and add up to 10??
Factored form: 𝑥+9 𝑥+1
*check by foil or box method

11. what can multiply to 12 and add up to 8??
11. 𝑥 2 +8𝑥+12
what can multiply to 12 and add up to 8??
Factored form: 𝑥+6 𝑥+2
*check by foil or box method

12. what can multiply to 5 and add up to 6??
12. 𝑥 2 +6𝑥+5
what can multiply to 5 and add up to 6??
Factored form: 𝑥+5 𝑥+1
*check by foil or box method

13. Factored form: 𝑥+3 𝑥+3 or 𝑥+3 2

14. We would call this PRIME.
18. One of the orders that Quinn wrote down was the following: 𝑥 2 +7𝑥+9. Quanyka says that she cannot make a rectangle with this area. Do you agree or disagree? How can you tell if a rectangle can be constructed from a given area?
She is correct. There is not a pair of numbers that will multiply to 9 and add up to 7.
We would call this PRIME.

15. 7.16 Quilt Blocks Galore!!
Less drawing, more labeling…

16. 𝑥+0 𝑥+2 or 𝑥(𝑥+2)
(𝑥+0)(𝑥−2) or 𝑥(𝑥−2)
(𝑥−1)(𝑥+3)

17. 4. 𝑥−2 𝑥+4 = 𝑥 2 +2𝑥−8
5. 𝑥+1 𝑥−3 = 𝑥 2 −2𝑥−3
6. 𝑥+3 𝑥−4 = 𝑥 2 −𝑥−12
7. 𝑥+4 𝑥−3 = 𝑥 2 +𝑥−12

18. 9. 𝑥+3 𝑥−3
10a. 𝑥 2 −1
10b. 𝑥 2 −25

19. 12a. 𝑥 2 −6𝑥+8
12b. 𝑥 2 −4𝑥+3

20. 14a. 𝑥 2 +7𝑥+10= 𝑥+5 𝑥+2
14b. 𝑥 2 +3𝑥−10= 𝑥+5 𝑥−2
14c. 𝑥 2 −2𝑥−24= 𝑥+4 𝑥−6
14d. 𝑥 2 −10𝑥+24= 𝑥−6 𝑥−4
14e. 𝑥 2 −6𝑥+5= 𝑥−5 𝑥−1
14f. 𝑥 2 −4𝑥−5= 𝑥−5 𝑥+1
14e. 𝑥 2 +5𝑥−14= 𝑥+7 𝑥−2

21. 𝑇𝑜 𝑓𝑎𝑐𝑡𝑜𝑟 𝑠𝑜𝑚𝑒𝑡ℎ𝑖𝑛𝑔 𝑖𝑛 𝑡ℎ𝑒 𝑓𝑜𝑟𝑚 𝑥 2 +𝑏𝑥+𝑐 𝑦𝑜𝑢 𝑛𝑒𝑒𝑑 𝑡𝑜 𝑓𝑖𝑛𝑑 𝑡𝑤𝑜 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑡ℎ𝑎𝑡 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦 𝑡𝑜 𝑐 𝑎𝑛𝑑 𝑎𝑑𝑑 𝑡𝑜 𝑏
**This only works because the a value is 1