1. Factoring Polynomials

2. Multiplying Polynomials
(x-5)(2x+1)
(y2 + 3y +6)(y-4)

3. Multiplying Polynomials
(x2 + 2) (x-8)
(y3-4)(y2 +3y-6)

4. Checklist
Greatest Common Factor
Leading coefficient a=1
ax2 +bx+c

5. Factoring 4x-20 =4(x-5) -3x2 +12x+27 =-3x(x-4x-9) =3x(-x+4x-9)
2(x-y)-a(x-y)
=(x-y)(2-a)

6. Factor
4x-48
63x3 + 7x2 +21x
2(x-y)-a(x-y)
x2 (x–5) + 4(5 –x)

7. Factor
b2 + 8b + 7
Diamond Way:
Multiply 7 1 7 8
Add
(x ) (x ) +1 +7

8. Factor using the Diamond
Check your Work
X2 + 4x -12
n2− n − 56
5v2− 30v + 40
(x2-81)

9. Factor Using the Diamond
Check your Work
n2+ 6n + 8
2x2+ 6n − 108
(x2-144)
x2 /3-x- 10/3

10. Activity Challenge the other groups Create 3 problems to factor Rules:
Needs to be a trinomial
Highest exponent is a 2
Can have a leading coefficient a=1
**Make sure you check your work**

11. Warm Up
Use the Diamond Method
4x2 + 8x – 60

12. Warm Up
Use the Diamond Method
1/2x2+x-15/2

13. Checklist Greatest Common Factor Leading coefficient a=1 ax2 +bx+c

14. Guess and Check
3x2-2x-5
( x )( x )

15. Practice
Check your work
5n2 -18n + 9
−6a2 − 25a − 25
16b2 + 60b − 100

16. Practice 5n2 -18n + 9 −6a2 − 25a − 25 16b2 + 60b − 100 1/3x2 +2/3x-8
Check your work
5n2 -18n + 9
−6a2 − 25a − 25
16b2 + 60b − 100
1/3x2 +2/3x-8

17. Box Method (only works if common factors have been removed)
2x2 + x − 6
Step 1: Multiply the leading coefficient and the constant
2(6)
=12
Step 2: Find the common factors:
Of 12
2x2 4x
-3x -6

18. 2x2 + x − 6 2x
2x2 4x
-3x -6 -3 -2 x
(2x-3)(x-2)

19. Factor
Use the box method
3x2 – 7x –6
5x2+ 19n + 12
7x2+ 53a + 28

20. Factor by Grouping 2 9 2n2+ 3n − 9
Step 1: Multiply the leading coefficient with the constant
2(-9)
=-18
Step 2: Find the factors of 18 that add to 3 2 9

21. 2n2+ 3n − 9
Step 3:
2n2+6n-3n − 9
Step 4: Split the polynomial down the middle
(2n2+ 6n)+(3n − 9)
Step 5: Greatest Common Factor
2n(n+3) + -3(n+3)

22. 2n2+ 3n − 9
2n(n+3) + -3(n+3)
Step 6: Common Factor
(n+3)(2n-3)

23. Practice 5n2 +19+12 -12f2 -38f+22 8x3 – 64x2 +x-8
12x2 u+3x2 v+28yu+7yv

24. Step 1) Multiply leading coefficient and constant
Factor
3x2 − 2x − 5
Slide and Divide:
Step 1) Multiply leading coefficient and constant
3 x2 − 2x − 5
-15

25. x2 − 2x − 15 Step 2) Use the Diamond Method (x ) (x ) -5 +3 -15 -5 3
Multiply
-15 -5 3 -2
Add
(x ) (x ) -5 +3

26. .
(x-5)(x+3) Step 3) Divide (x- ) (x+ ) Step 4) Simplify (x- ) (x+3) Step 5) Multiply (3x-5)(x+3) ─

27. Factor
2v2 + 11v + 5
3m2 – 10m + 8
15 m3 +24m2 +9m
2y^2(4x^2+9)