A Method For Simple Cases For Factoring A Quadratic

A Method For Simple Cases For factoring a Quadratic

Luckily there is a method that works in simple cases. With the quadratic equation in this form:

Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b.

OK, let us try another example:

Example: 6x² + 5x 6

Step 1: ac is 6 ( 6) = 36, and b is 5

List the positive factors of ac = 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

One of the numbers has to be negative to make 36, so by playing with a few different numbers I find that 4 and 9 work nicely:

4 9 = 36 and 4+9 = 5

Step 2: Rewrite 5x with 4x and 9x:

6x² 4x + 9x 6

Step 3: Factor first two and last two:

2x(3x 2) + 3(3x 2)

Step 4: Common Factor is (3x 2):

(2x+3)(3x 2)

Check: (2x+3)(3x 2) = 6x² 4x + 9x 6 = 6x² + 5x 6 (Yes)

This resource was uploaded by: Adrian