1. Warm-up: Pick up a calculator
Find the greatest common factor.
12x2 + 6x m2 – 35m v3 + 36v2 + 10
12x2 + 6x 12x2 = 2 • 2 • 3 • x • x;
6x = 2 • 3 • x; GCF = 2 • 3 • x = 6x
28m2 – 35m m2 = 2 • 2 • 7 • m • m;
35m = 5 • 7 • m;
14 = 2 • 7; GCF = 7
4v3 + 36v2+10 4v2 = 2 • 2 • v • v;
36v2 = 2 • 2 • 3 • 3 • v • v;
10 = 2 • 5 GCF = 2

2. Remind ALL Make Up WORK due next Friday, May 25th!!!
HW Check:
Collect Worksheet
Collect Q4 W7 Warmups
Remind ALL Make Up WORK due next Friday, May 25th!!!

3. HW Check

4. HW Check 7. 8. 9.
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5. HW Check
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6. HW Check
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7. 7.15 Factoring with X-Box
Objective:
To explore factoring.

8. X-box Factoring

9. X- Box ax2 + bx + c Trinomial (Quadratic Equation)
Product of a & c
ax2 + bx + c
Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. b

10. X- Box x2 + 9x + 20 Trinomial (Quadratic Equation)
Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. 5 4 9

11. X- Box 2x2 -x - 21 Trinomial (Quadratic Equation)
-42
Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. 6 -7 -1

12. X-box Factoring
This is a guaranteed method for factoring quadratic equations—no guessing necessary!
We will learn how to factor quadratic equations using the x-box method

13. LET’S TRY IT!
Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
Objective: I can use the x-box method to factor non-prime trinomials.

14. Factor the x-box way x2 -5x -10 2x Example: Factor x2 -3x -10 -5
(1)(-10)=
-10 x x2
-5x x
GCF -5 2 -3 2x
-10 +2
GCF
GCF
GCF
x2 -3x -10 = (x-5)(x+2)

15. First and Last Coefficients
Factor the x-box way
y = ax2 + bx + c
GCF
GCF
Product
ac=mn
First and Last Coefficients
1st Term
Factor n
GCF n m
Middle
Last term
Factor m
b=m+n
Sum
GCF

16. Factor the x-box way Example: Factor 3x2 -13x -10 x -5 -30 3x 3x2 -15x+2
3x2 -13x -10 = (x-5)(3x+2)

17. Examples Factor using the x-box method. 1. x2 + 4x – 12 x +6 x2 6x x
-12 4
x x
-2x x 6 -2 -2
Solution: x2 + 4x – 12 = (x + 6)(x - 2)

18. Examples continued x -4 x x2 -4x -5x 20 20 -9 x
x2 -4x
-5x 20 -5
Solution: x2 - 9x + 20 = (x - 4)(x - 5)

19. Examples continued 2x -7 x 2x2 -7x 2x -7
-14 -5 x
2x2 -7x
2x -7 +1
Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

20. Examples continued 3x +2 5x 15x2 10x -3x -2
a) b) 3x +2
-30 7 5x
15x2 10x
-3x -2 -1
Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

21. You Try… #1
By Hand
(x+8)(x-4)
x2 +4x -32

22. #2
By Hand
4x2 +4x -3
(2x+3)(2x-1)

23. #3
By Hand
3x2 + 11x – 20
(3x-4)(x+5)

24. (x + 1)(x+5)
(3x-2)(3x+1)
(3a-2)(2a+1)
Not Factorable
(x-4)(x+4)

25. Don’t forget to check your answer by multiplying!
Reminder!!
Don’t forget to check your answer by multiplying!

26. The Grouping Method!!

27. backwards
Demonstrate
3(8) = 24
add to equal 10
standard
First two
Last two
GCF
GCF

28. (x + 3)(x+4)
(x - 1)(7x+2)
Not Factorable
(x + 5)(x-5)
(2y + 1)(y - 7)

29. Classwork:
7.15 Factoring a=1 WS
Homework:
7.15 p RSG