1. Factoring Trinomials
When a 1

2. Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms
1. GCF 2 or more
2. Diff. Of Squares 2
Trinomials 3
Grouping

3. Review: (3y + 2)(y + 4) Multiply using FOIL.
Combine like terms.
3y² + 12y + 2y + 8 =
3y² + 14y + 8
y² + (12 + 2)y + (2)(12)
How would you get 24 from the 2nd step?
*You need the factors of ac that add to = b.

4. ax2 + bx + c * If p and q are factors of ac that add to = b and p > q. ax2 + bx + c ax2 - bx + c (x+p)(x+q) (x-p)(x-q) ax2 + bx – c ax2 – bx - c (x+p)(x-q) (x-p)(x+q)

5. 1) Factor. 3y2 + 14y + 8 Create a table as shown below.
Factors of ac: Multiply the 1st and last coefficients: 3(8) = 24
Sum of b: Middle coefficient: 14
Factors of Sum of +14
1, 24
2, = 14*
3, 8
4, 6

6. now divide or reduce 12 and 2 by your a (a= 3)
Factor. 3y2 + 14y + 8
( x + 12) (x + 2)
now divide or reduce 12 and 2 by your a (a= 3)
___
___ 3 3
( x + 12) (x + 2) *After you reduce, if there is a number left in the denominator, you take it to the front of the factor.

7. ___
___
( x + 12) (x + 2) 3 3
= ( x + 4) (3x + 2) y

8. 2) Factor. 5x2 - 17x + 14 Factors of: Multiply the 1st and
last coefficients.
Sum of: Middle Term
Factors of Sum of -17

9. Factor. 5x2 - 17x + 14 Factors of +70 Sum of -17
-10,
( x - 10) (x – 7)
now reduce 10 and 7 by your a (a= 5)

10. ___
___ 5 5
( x - 10) (x – 7) *After you reduce, if there is a number left in the denominator, you take it to the front of the factor.
=( x - 2) (5x – 7)

11. FACTORING
QUIZ

12. It is not the easiest of things to do, but the more problems you do, the easier it gets! Trust me!
3) Factor. 2x2 + 9x + 10
(2x + 5)(x + 2)

13. 1st Step: Check to Factor GCF
12y2 - 26y – 10
****Do not forget**
1st Step: Check to Factor GCF
GCF: 2
2( 6y2 - 13y – 5)

14. Now we need to find the factors of ac that + to = b
2( 6y2 - 13y – 5)
Now we need to find the factors of ac that + to = b
Factors of ac: a=6 and c = -5
so ac = -30.
Sum of b: -13

15. 2( 6y2 - 13y – 5)
Factors of Sum of -13
1, -30
2, = -13
3, -10
5, -6

16. Now reduce by the a term (a = 6) 2(y + 2)(y – 15)
___
___ 6 6
2 ( y + 1)( y – 5)
___
___ 3 2
2(2y-5)(3y+1)

17. 5) -12x2 - 11x + 5
-(3x-1)(4x+5)
6) 5x x2
1st reorder: x2 + 5x - 6
(x-1)(x+6)