1. Homework Help
Ch 8-4

2. Multiply a times c to find the product. –3
All of the previous problems involving quadratic trinomials had a leading coefficient of 1.
Multiply a times c to find the product. –3 –3 1 –2
b in the bottom represents the sum
Check by doing FOIL in your head!
You know there will be an x in each factor!
You know there will be an x in each factor!

3. Today’s problems involve factoring quadratic trinomials when the leading coefficient isn’t 1 - this includes negative 1.
To factor quadratic trinomials when the leading coefficient isn’t 1, you will use the X figure and then factor out the greatest monomial factor.

4. Step 1 Use the X figure as you did when the leading coefficient was 1.
–10
Multiply a times c to find the product.
– 5 –5
+ 2 2 –3
b in the bottom represents the sum
Step 2 Take the coefficient “a” and the x from the ax2 term and the numbers from the sides of your X figure and place them into two parentheses in the following manner.
( )( )
Step 3 Factor out the greatest monomial factor from each parentheses if you can.
Step 4 Discard the monomial factor/s you pulled out.
Step 5 Check using FOIL.

5. –3 –10 2 – 5 –5 + 2 ( )( ) Check using FOIL.
You must throw away the greatest monomial factor that is pulled out after using the X figure!
( )( )
Check using FOIL.

6. DO NOT DISCARD THIS FACTOR!
Before you use the X figure, you must factor out any greatest monomial factor, if possible!
You must keep the greatest monomial factor that is pulled out before using the X figure!
DO NOT DISCARD THIS FACTOR!

7. Factor.
-10
- 5 -5
+ 2 2 -3
( )( )
If you factor out a GMF:
before using the X figure, keep it,
after using the X figure, discard it.
Check using FOIL.

8. Factor out a GMF before the X figure – you must keep it!
Factor out a GMF after the X figure – discard it!

9. Can you factor out a greatest monomial factor?
Example 1 Factor. 6
+ 3 3
+ 2 2 5
Can you factor out a greatest monomial factor?
( )( )
Check using FOIL.

10. before using the X figure, keep it,
Factor.
Example 2
Example 3
-22
-18
+ 22 22
- 1 -1
Can you factor out a greatest monomial factor?
Can you factor out a greatest monomial factor?
+ 6 6
- 3 -3 21 3
( )( )
( )( )
Check using FOIL.
If you factor out a GMF:
before using the X figure, keep it,
after using the X figure, discard it.

11. Factor. Example 4 Example 5 36 -12 + 9 9 + 4 4 - 6 -6 + 2 2 13 -4
Can you factor out a greatest monomial factor?
Can you factor out a greatest monomial factor? 13 -4
( )( )
( )( )
Check using FOIL.
Check using FOIL.

12. Homework
445 # 11 – 30
Graph: