1. Factoring Quadratic Trinomials Part 1 (when a=1 and special cases)

2. Factoring Trinomials:
Factoring is the opposite of distributing
To factor a trinomial, turn it back into its factored form
(the 2 binomials it came from)
Quadratic Standard Form ax2+bx+c
ex. 2x2+2x-12
Quadratic Factored Form
(x-r1)(x-r2)
ex. (2x-4)(x+3)

3. Steps to Follow: 1. Factor out a GCF if possible 2. Set up a t-chart
3. Multiply a*c and list factors of that number (today we will only do problems when a=1, so just list factors of c)
4. Add those factors together and select the pair that adds to “b”
5. Write answer in factored form (x± )(x ± )
a*c b
list pairs of factors of c here
Add up those factors and write the sum here

4. What two numbers multiply to “ac”
Think to yourself:
What two numbers multiply to “ac”
AND
Add to “b“
Use the t-chart to help organize your thinking

5. Factor x2-x-12 (x+3)(x-4) ac b Check for GCF -12 -1 Set up t-chart
1 (-12)
= -11
List factors of ac (in this case one will need to be + and one – )
Add those factors and select the pair that adds to b +
-1 (12)
= 11
-2 (6) +
= 4 +
2 (-6)
= -4 +
3 (-4)
= -1
-3 (4)
(x+3)(x-4)

6. How can you predict the sign of the factors that will work?
x2- 5x + 6 ac 6 b -5
1 (6) 7 -7
-1 (-6)
How can you predict the sign of the factors that will work?
2 (3) 5
-2 (-3) -5
(x - 2)(x - 3)

7. Factor prime x2 + 3x + 7 ac b 7 3 1 (7) 8 -8 -1 (-7)
If there aren’t factors that work, it is prime (meaning it cannot be factored into integers)
prime

8. Factoring is the opposite of distributing
So x2 + 5x + 6 factored is (x+3)(x+2)
x2 + x - 6 factored is (x-2)(x+3)

9. Factoring Special Products
Remember the Special Cases?
Use the same patterns in reverse:
Perfect Square Trinomial:
a2 ± 2ab ± b2 = (a ± b) 2
Difference of Perfect Squares:
a2 - b2 = (a+b) (a-b)

10. Perfect Square Trinomial Pattern
Factor
*Look to see if:
-first and last terms are perfect squares
-and middle term is 2ab
*If follows pattern, it will factor into
Square root first term and make that a
Square root last term and make that b

11. FACTOR: (4y + 3)2 Perfect square polynomial:
Square root first term and make that a
Square root last term and make that b
Check that middle term is 2ab
Perfect square polynomial:
(4y + 3)2

12. Difference of perfect squares: (9-3x2)(9+3x2)

13. Doesn’t factor, no common factor except 1!
Prime

14. Perfect square polynomial: