1. 8-4A Factoring Trinomials when the Leading Coefficient isn’t 1.
X-Factor method
Algebra Glencoe McGraw-Hill Linda Stamper

2. Factoring quadratic trinomials means finding the binomial factors when given a product. The factors represent the length and width of the rectangle.
You need to find the factors!
You need to find the factors!
x + 2
You are given the product – quadratic trinomial!

3. 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!

4. 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 (aka greatest common factor).

5. 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 factor/s you pull out after X figure.
Step 5 Check using FOIL.

6. –3 –10 2 – 5 –5 + 2 ( )( ) Check using FOIL.
You must discard (X out) the GMF that is pulled out after using the X figure!
( )( )
Check using FOIL.

7. 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 GMF that is pulled out before using the X figure!
DO NOT DISCARD THIS FACTOR!

8. 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.

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

10. Try this problems... 5 –4
A polynomial that cannot be written as a product of two polynomials with integral coefficients is called a prime polynomial!

11. Copy all of the above problems before you start to factor!
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Copy all of the above problems before you start to factor!

12. 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.

13. 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.

14. Factor. Example 4 Example 5 36 + 9 9 + 4 4 13 ( )( ) Check using FOIL.
Can you factor out a greatest monomial factor?
Can you factor out a greatest monomial factor? 13
( )( )
Check using FOIL.

15. Factor. Example 6 Example 7 280 -12 - 6 -6 + 2 2 -8 -35 -4 -43
Make an organized list of factors.
1•280
2•140
4 •70
5 •56
7 •40
8 •35
280
-12
- 6 -6
+ 2 2 -8
-35
Can you factor out a greatest monomial factor?
Can you factor out a greatest monomial factor? -4
-43
(10x - 8)(10x - 35)
( )( )
Check using FOIL.
Check using FOIL.

16. Factor.
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7

17. Homework
8-A9 Page # 11–22,44,46-51.