1. September 21, 2017
Multiply the following factors on an index card.
(𝟕𝒙+𝟑)(𝟖𝒙−𝟒)

2. X-box Factoring

3. Factor the x-box way y = ax2 + bx + c (x + m)(x + n) Product ac=mn m n
First and
ac=mn
Last Coefficients m n
b=m+n
Sum

4. X- Box
(x + 3)(x - 9)
Product x + 3 -9
Sum

5. y = x2 + 7x + 12 y = x2 + 3x - 10 y = x2 - 7x - 18 y = x2 - 10x + 24
-10 x + 7 x + 3
-18 24 x + -7 x +
-10
y = x2 - 7x - 18
y = x2 - 10x + 24

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

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

8. Examples continued 2. x2 - 9x + 20
-4 -5 -9
Solution: x2 - 9x + 20 = (x - 4)(x - 5)

9. Examples continued Examples continued 3. 2x2 - 5x - 7
-14
-7 2 -5
Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

10. Examples continued 4. 15x2 + 7x - 2
-30 7
Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

12. GCF Greatest common Factor
What is the greatest common factor of each pairs of monomials?
15y and 30y2
-5a2b2 and -3ab?
Use your answer to factor each of these.
15y + 30y2
-5a2b2 + -3ab?

13. 5.4.2 Factoring Out a Negative Factor.

15. Grouping
𝑥 4 +2 𝑥 3 − 𝑥 2 −2𝑥−9𝑥−18

16. Continued

17. 5.4.4 Factor by Grouping

18. 5.4.4 Factor By Grouping

19. 5.4.4 Factor By Grouping

20. 5.4.4 Factor By Grouping

21. Always factor out the GCF first if you can!
5.4.4 Factor By Grouping
Always factor out the GCF first if you can!

22. You may have to rearrange terms.
5.4.4 Factor By Grouping
You may have to rearrange terms.

23. Factor By Grouping