Factoring By Grouping

Definition: To factor a quadratic using the grouping method, pull out any common factors then rewrite the equation in a way that will allow us to pull a common factor out of each group. If you need a refresher on quadratic equations, click here.

Example: Factor the following quadratic: 6x² – 26x – 20

Solution: 

Step 1: Determine if the terms have a common factor. Our terms are 6x², -26x and -20, which have a common factor of 2:

6x² – 26x – 20 = 2(3x² – 13x – 10)

Step 2: Rewrite the equation in a way that will allow us to regroup and find a common factor. Since we are looking for a numbers with a sum of b (-13) and a product of ac (-30), we can use -15 and 2.

2(3x² – 13x – 10) = 2(3x² – 15x + 2x – 10)

Step 3: Group terms into pairs using parenthesis and pull out any common factors:

2[(3x² – 15x) + (2x – 10)] = 2[3x(x – 5) + 2(x – 5)]

Step 4: Pull the common factor (x-5) out of each group:

2(x-5)(3x+2)

Step 5: Multiply to check:

2(x – 5)(3x + 2) = 2(3x*x -5*3x + 2x – 5*2) = 2(3x² – 15x + 2x – 10) = 6x² – 26x – 20

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