1. RULES FOR FACTORING Step 1: CMF Step 2: Binomial? DOTS?
Step 3: Trinomial?
PST?
Guess Method

2. RULES FOR FACTORING REVIEW OF CMF 6x2 – 12 = 6 (x2 – 2)3
(x2 – 2x + 6)
10x3 + 15x2 – 5x = 5x
(2x2 + 3x – 1)

3. Difference Of Two Squares
D.O.T.S.
Difference Of Two Squares
Perfect Squares
Difference
means subtract x2 9
9x2
So, examples
of DOTS: y2 16
25y2 a2 49
81x2y2
x2 – 16 b6
100
4x4y6 or
4a2 – 25b2

4. D.O.T.S.
FLASH CARDS
Is it DOTS?
x2 – y2 D

5. D.O.T.S.
FLASH CARDS
Is it DOTS?
a2 – 9 D

6. D D.O.T.S. 6m2 – 81 FLASH CARDS Is it DOTS? Why not?
6 IS NOT A PERFECT SQUARE!

7. D D.O.T.S. 4b2 + 25 FLASH CARDS Is it DOTS? Why not?
THIS IS A SUM OF 2 SQUARES.

8. D.O.T.S.
FLASH CARDS
Is it DOTS?
49b2 – 100c4 D

9. Difference Of Two Squares
D.O.T.S.
Difference Of Two Squares
DOTS always factors the same way.
(Square root of the first + square root of the last) times
(Square root of the first – square root of the last)
Example:
x2 – 16 = (x + 4) (x – 4)

10. Difference Of Two Squares
D.O.T.S.
Difference Of Two Squares
4a2 – 25b2
= (2a + 5b)
(2a – 5b)
b2 – 49
= (b + 7)
(b – 7)
9x2y2 – 64b6
= (3xy + 8b3)
(3xy – 8b3)

11. P.S.T. Perfect Square Trinomial How to identify: x2 + 6x + 9 x 3x 3
☺1st & last term must
be perfect squares
YES!
x2 + 6x + 9
☺Square root of the first ?
☺Square root of the last x 3x 3
☺Multiply them
☺Double the result
☺Is it the same as the middle term?(disregard sign)

12. PST THIS IS A P.S.T. Perfect Square Trinomial How to identify:
☺1st & last term must
be perfect squares
x2 + 6x + 9
THIS
☺Square root of the first ?
☺Square root of the last x 3x 3 IS
☺Multiply them A
PST
☺Double the result
☺Is it the same as the middle term?(disregard sign)

13. D.O.T.S.
FLASH CARDS
Is it PST?
x2 – 10x + 25
U BETCHA

14. D.O.T.S.
FLASH CARDS
Is it PST?
x2 – 10x – 25
NO WAY
DO YOU KNOW WHY?

15. D.O.T.S.
FLASH CARDS
Is it PST?
x2 + 20x + 40
NO WAY
DO YOU KNOW WHY?

16. D.O.T.S.
FLASH CARDS
Is it PST?
9m2 + 42m + 49
U BETCHA

17. D.O.T.S.
FLASH CARDS
Is it PST?
x2 + 16xy + 64y2
U BETCHA

18. What would make this a PST?
D.O.T.S.
FLASH CARDS
What would make this a PST?
±12x
x2 _____ + 36

19. What would make this a PST?
D.O.T.S.
FLASH CARDS
What would make this a PST?
±36xy
4x2 _______ + 81y2

20. What would make this a PST?
D.O.T.S.
FLASH CARDS
What would make this a PST?
x2 – 6x ____
+ 9

21. Perfect Square Trinomial Square root of the first
P.S.T.
Perfect Square Trinomial
How to factor
x2 + 6x + 9
Square root of the first (x + 3)
Sign of the second term 2
Square root of the last
Quantity squared

22. Perfect Square Trinomial Square root of the first
P.S.T.
Perfect Square Trinomial
How to factor
4m2 – 20m + 25
Square root of the first
(2m – 5)
Sign of the second term 2
Square root of the last
Quantity squared

23. 5x2 + 10xy 5x(x + 2y) FLASH CARDS Factoring Practice RECALL STEPS! 1.
CMF 2.
BINOMIAL?
DOTS
5x(x + 2y) 3.
TRINOMIAL
PST
GUESS

24. x2 – 9y2 (x + 3y)(x – 3y) FLASH CARDS Factoring Practice RECALL STEPS!1.
CMF 2.
BINOMIAL?
DOTS
(x + 3y)(x – 3y) 3.
TRINOMIAL
PST
GUESS

25. 4x2 – 28x + 49 (2x – 7)2 FLASH CARDS Factoring Practice RECALL STEPS!1.
CMF 2.
BINOMIAL?
DOTS
(2x – 7)2 3.
TRINOMIAL
PST
GUESS

26. a2 – 2a – 15 (a – 5)(a + 3) FLASH CARDS Factoring Practice
RECALL STEPS!
a2 – 2a – 15 1.
CMF 2.
BINOMIAL?
DOTS
(a – 5)(a + 3) 3.
TRINOMIAL
PST
GUESS

27. FLASH CARDS Solving Equations 2x3 + 8x2 – 42x = 0 2x(x2 + 4x – 21) = 0
Set equal to zero:
Already is!
Factor left side:
2x(x2 + 4x – 21) = 0
2x(x + 7)(x – 3) = 0
More Factoring??
Factors = to 0:
2x= 0 or x + 7 = 0 or x – 3 = 0
Solve equations:
x= 0 or x = -7 or x = 3