1. X-box Factoring to Solve Quadratic Equations1

2. Warm-up: X- Box Puzzles? 50 5
-12 ? ? ?
-15

3. Activator: What was the problem? What is the answer?
Problem: 6x2 + x - 1
Answer: (3x – 1)(2x + 1)

4. Essential Question
How do I use an X box strategy to solve quadratic equations like ax2 + bx + c = 0, when a ≠ 1?

5. Recall: Factor the x-box way
y = ax2 + bx + c
Base 1
Base 2
Product
ac=mn
First and Last Coefficients
1st Term
Factor n
GCF n m
Middle
Last term
Factor m
b=m+n
Sum
Height
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6. Examples Factor using the x-box method. x2 + 4x – 12 x +6 -12 4 x2 6x
a) b) x +6
-12 4
x2 6x
-2x -12 x 6 -2 -2
Solution: x2 + 4x – 12 = (x + 6)(x - 2)

7. Examples continued 2x2 - 5x + 3 2x -3 x 2x2 -3x -2x 3
a) b) 2x -3
-3x -2x 6 -5 x
2x2 -3x
-2x 3 -1
Solution: 2x2 - 5x + 3 = (2x - 3)(x - 1)

8. Examples continued Factor: 2x2 - 5x - 7 2x -7 x 2x2 -7x 2x -7
a) b) 2x -7
-14 -5 x
2x2 -7x
2x -7 +1
Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

9. Summarize
Factor: 3x2 + 11x – 20 and formalize the steps.

10. Partner Practice
Grab your white boards, pens and erasers! Do the Checkpoint Problems #1,2,3 p. 603

11. Written Practice
Grab your white boards, pens and erasers! Do the Checkpoint Problems #4-9 p. 604

12. Exit Ticket
Factor the trinomials:
4x2 + 8x x2 – 9x + 2

13. Homework
Do the worksheets for Homework using the X-box method. Show all your work to receive credit– don’t forget to check by multiplying!