Module 7.15 Quanyka’s Quilts

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

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

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

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

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

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)

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 12 + 2 = 14 There are 2 inches on this side 𝐴 𝑥 = 𝑥 2 +14𝑥+24 𝐴 𝑥 =(𝑥+12)(𝑥+2)

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

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

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

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

Factored form: 𝑥+3 𝑥+3 or 𝑥+3 2

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.

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

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

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

9. 𝑥+3 𝑥−3 10a. 𝑥 2 −1 10b. 𝑥 2 −25

12a. 𝑥 2 −6𝑥+8 12b. 𝑥 2 −4𝑥+3

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

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