1. Apply basic factoring techniques to second degree polynomials
Notes Lesson 10-3
Lesson 6-5
Factoring ax2 + bx + c
Standard 11.0
Apply basic factoring techniques to second degree polynomials
Taken from:
Rebecca Renken, Mathematics Department, Francis Howell High School

2. Example 1
Factor 17x x2
Before factoring a trinomial it must be written in descending order
You must always look for the greatest common factor first…it may be a negative.
The coefficient of the squared term must be positive.
If the coefficient of the squared term is greater than one that is what tells you to use the box and diamond method

3. Example 1 Solution Box and Diamond Method
Factor 17x x2  3x2 + 17x + 10, no greatest common factor
Draw a box put the first and last term diagonal from each other
Then multiply the coefficients together and this will give you the number for the north
3x2 10

4. Example 1 Solution Box and Diamond Method
3x2 + 17x + 10
3x2∙10 = 30x2
What can you multiply to get 30 that adds up to 17? 30
The coefficient of the middle term is in the south
3x2 10 17

5. Example 1 Solution Box and Diamond Method
3x2 + 17x + 10
3x2∙10 = 30x2
What can you multiply to get 30 that adds up to 17?
Put those same two terms in your box multiplied by the variable
3x2 10 30 2 15 17

6. Example 1 Solution Box and Diamond Method
3x2 + 17x + 10
Now factor out the greatest common factor from each row and column
The signs from your diamond apply to the box
3x2 10 30
15x 2 15 2x 17

7. Example 1 Solution Box and Diamond Method
3x2 + 17x + 10
Now factor out the greatest common factor from each row and column
The signs from your diamond apply to the box x +5
3x2 10 30 3x
15x 2 15 +2 2x 17
The answer is (3x + 2)(x + 5)

8. Example 2
Factor 12x2 + x - 6

9. Example 2 12x2 -6 Factor 12x2 + x – 6 The answer is (4x + 3)(3x – 2)-2
12x2 -6
-72 4x
-8x -8 9 9x 1 +3

10. Example 3
Factor 30x2 -23x +3
The answer is

11. Example 3 30x2 3 Factor 30x2 -23x +3 The answer is (6x - 1)(5x – 3) 5x-3
30x2 3 90 6x
-18x -5
-18
-5x
-23 -1

12. Things to Remember Always check for the GCF…it might be negative.
The signs of the numbers in the “west” and “east” indicate the signs that must be in your parentheses.
Check your work by using the FOIL method.

13. Burning Questions??