1. 8.6 Day 1 Notes
Factoring
𝒙 𝟐 +𝒃𝒙+𝒄

2. Warm-up
Solve for y in the following equations. 1) 16y2 – 20y = 0 2) 6y2 = 9y What is different about the two equations above? Why does this matter?

3. Factoring! Factoring 𝒙 𝟐 +𝒃𝒙+𝒄 (Product/Sum)
You have learned how to multiply two binomials. Each of the binomials was a factor of the product.
Factoring 𝒙 𝟐 +𝒃𝒙+𝒄
(Product/Sum)

4. Example 1
Factor each polynomial. a) x2 + 7x + 12 b) x2 – 12x + 27 c) x2 + 3x – 18

5. Warm-up
Factor each of the following expressions. 1) x2 – 6x – 16 2) x2 + 2x – 8

6. Example 1
Factor each polynomial. Remember to check for the GCF first!! a) 2 𝑥 2 +12𝑥+16 b) 3 𝑥 2 −6𝑥−45 c) 2 𝑥 2 +14𝑥+24

7. Extra Practice!
Factor each polynomial. Remember to check for the GCF first!! a) x2 – 10x + 16 b) x2 – x – 20 c) 𝑥 2 +5𝑥+6

8. Extra Practice!
d) 𝑥 2 −7𝑥−18 e) 5 𝑥 2 +25𝑥+20 f) 4 𝑥 2 −4𝑥−8

9. Extra Practice!
g) 𝑥 2 −7𝑥+10 h) 𝑥 2 +13𝑥+12 i) 2 𝑥 2 +2𝑥−4

10. Warm-up
Factor each of the following expressions. 1) 𝑥 2 −7𝑥+10 2) 2 𝑥 2 +4𝑥−30

11. Vocab!
Quadratic Equation

12. Example 3-Solving without GCF
Solve each equation. Check your solutions. a) x2 + 2x = 15 b) x2 – 20 = x c) x2 + 4x + 27 = 24

13. Example 4-Solving with GCF
Solve each equation. Check your solutions. a) 4 𝑥 2 +4𝑥=24 b) 2 𝑥 2 −6𝑥=20 c) 2 𝑥 2 +60=−22𝑥

14. Example 5-Application
Marion wants to build a new art studio that has three times the area of her old studio by increasing the length and width by the same amount. What should be the dimensions of the new studio?

15. Example 6-Application
Adina has a 4 × 6 photograph. She wants to enlarge the photograph by increasing the length and width by the same amount. What dimensions of the enlarged photograph will produce an area twice the area of the original photograph?

16. Example 7 Which equation has roots of −4 and 7? (MC)
a) (𝑥−4)(𝑥+7) b) 𝑥−4 𝑥−7
c) 𝑥+4 𝑥− d) 𝑥+4 𝑥+7

17. Summary