Slide, Divide, Bottoms Up (SDB) |
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: 3x^{2} + 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: x^{2} + 8x + (3)(4); x^{2} + 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
(3x + 2) (x + 2) 3x^{2} |
(3x + 2) (x + 2) 6x |
(3x + 2) (x + 2) 2x |
(3x + 2) (x + 2) 4 |
3x^{2} + 6x + 2x + 4
3x^{2} + 8x + 4
Example 2: 9x^{2} - 6x - 15
Step 1) GCF: Every number is divisible by 3, so let's factor it out --> 3 ( 3x^{2} - 2x - 5)
Step 2) Slide "a" to "c" and multiply: 3 (x^{2} - 2x - (3)(5)); 3 ( x^{2} - 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
3 (3x - 5) (x + 1) 3x^{2} |
3 (3x - 5) (x + 1) 3x |
3 (3x - 5) (x + 1) -5x |
3 (3x - 5) (x + 1) -5 |
3 (3x^{2} + 3x - 5x - 5)
3 (3x^{2} - 2x - 5)
9x^{2} - 6x - 15