1. Factoring Trinomials Continued
Method of Decomposition

2. Method of Decomposition
Recall: Factoring Trinomials is working backwards from FOIL
F – first term
O – outside terms
I – inside terms
L – last terms
(x-8)(x+5)
F: (x)(x)=x2
O: (x)(5)=5x
I: (-8)(x)= -8x
L: (-8)(5)=-40
X2+ 5x - 8x - 40

3. Think about how you factor:
You want two numbers that MULTIPLY to give you the last term
The same two numbers ADD to give you the middle term
(x-8)(x+5)
F: (x)(x)=x2
O: (x)(5)=5x
I: (-8)(x)= -8x
L: (-8)(5)=-40
X2+ 5x - 8x – 40
X2 -3x - 40
Therefore:
Product of - 40
Sum of -3
(x – 8)(x + 5)

4. Method of Decomposition
Use this to decompose the trinomial
When there is a number besides one in the front we do the follow:
8x2 + 10x + 3
You multiply the first constant by the last constant to get the product.
8x2 + 4x + 6x + 3
= (8x2 + 4x) + (6x + 3)
= 4x(2x + 1) + 3(2x + 1)
=(2x + 1)(4x + 3)
Product is + 24
8x2 + 10x + 3
+6 and +4 give the product of + 24
6x + 4x
Which gives: 8x2 + 4x + 6x + 3

5. Factor: 6y2 + 19y + 15 6y2 + 19y + 15 = 6y2 + 9y + 10y + 15
Solution:
Think: What two integers have a product of +90 and a sum of +19.
The numbers are +10 and +9
6y2 + 19y + 15
= 6y2 + 9y + 10y + 15
= (6y2 + 9y) + (10y + 15)
= 3y(2y + 3) +5(2y + 3)
= (2y + 3)(3y + 5)
Group to factor
Factor each bracket
Collect common Factors
Expand to check solution is correct

6. Factor: 9x2 – 9x - 4 9x2 – 9x - 4 = = ( ) + ( ) You Try: Solution:
Think: What two integers have a product of -36 and a sum of -9.
The numbers are ? and ?
9x2 – 9x - 4 =
= ( ) + ( )
Group to factor
Factor each bracket
Collect common Factors
Expand to check solution is correct

7. Factor: 9x2 – 9x - 4 9x2 – 9x - 4 = 9x2 -12x + 3x - 4
Answer:
Solution:
Think: What two integers have a product of -36 and a sum of -9.
The numbers are -12 and + 3
9x2 – 9x - 4
= 9x2 -12x + 3x - 4
= (9x2 + 3x) + (-12x - 4)
= 3x(3x + 1) -4(3x + 1)
= (3x + 1)(3x – 4)
Group to factor
Factor each bracket
Collect common Factors
Expand to check solution is correct

8. Factor: 5x2 + 8x - 4 5x2 +8x - 4 = = ( ) + ( ) You Try: Solution:
Think: What two integers have a product of -20 and a sum of +8.
The numbers are ? and ?
5x2 +8x - 4 =
= ( ) + ( )
Group to factor
Factor each bracket
Collect common Factors
Expand to check solution is correct

9. Try this:
4y2 - 16y + 7