Slide, Divide, Bottoms Up (SDB)
This factoring technique can your best friend when it comes to factoring quadratic expressions. This is normally used when "a" has a value greater than 1. Below are the steps on the method.

Step 1: GCF
Step 2: Slide "a" to "c" and multiply
Step 3: Find factors of "c" that give the value of "b"; write as two binomials
Step 4: Divide factors by original "a" value and reduce fraction
Step 5: Bring the Bottoms of the fraction Up to front of binomial
Step 6: Check!

This may seem confusing, but it's do an example.

Example 1: 3x2 + 8x + 4
Step 1) GCF: We do not have a GCF so we can move on to step 2.
Step 2) Slide "a" to "c" and multiply: x2 + 8x + (3)(4); x2 + 8x + 12
Step 3) Find factors of "c" that add up to "b": 2, 6--> (x + 2) (x + 6)
Step 4) Divide factors by original "a": (x + 2⁄3) (x + 6⁄3)--> (x + 2⁄3) (x + 2)
Step 5) Bring the bottoms of the fraction to front of binomial: (3x + 2) (x + 2)

CHECK: using FOIL

F

(3x + 2) (x + 2)

3x2

O

(3x + 2) (x + 2)

6x

I

(3x + 2) (x + 2)

2x

L

(3x + 2) (x + 2)

4


3x2 + 6x + 2x + 4

3x2 + 8x + 4

Example 2: 9x2 - 6x - 15
Step 1) GCF: Every number is divisible by 3, so let's factor it out --> 3 ( 3x2 - 2x - 5)
Step 2) Slide "a" to "c" and multiply: 3 (x2 - 2x - (3)(5)); 3 ( x2 - 2x - 15)
Step 3) Find factors of "c" that add up to "b": -5, 3--> 3 (x + -5) (x + 3)--> 3 (x - 5) (x + 3)
Step 4) Divide factors by original "a": 3 (x - 5⁄3) (x + 3⁄3)--> 3 (x - 5⁄3) (x + 1)
Step 5) Bring the bottoms of the fraction to front of binomial: 3 (3x - 5) (x + 1)

CHECK: using FOIL

F

3 (3x - 5) (x + 1)

3x2

O

3 (3x - 5) (x + 1)

3x

I

3 (3x - 5) (x + 1)

-5x

L

3 (3x - 5) (x + 1)

-5


3 (3x2 + 3x - 5x - 5)

3 (3x2 - 2x - 5)

9x2 - 6x - 15