To factor by grouping first separate the equation into two groups and factor out the common factors from each group. Then combine the the common factors that are extracted from each group.
Example:
x^3 - 3x^2 + 2x - 6
1) First, separate it into two groups
(x^3 - 3x^2) + (2x - 6)
The common factor in this group is x^2 and if you take that out what is left is (x-3)
x^2(x-3)
3) Now factor out the common factors from (2x - 6)
The common factor in this group is 2 and if you take that out what is left is (x-3)
2(x-3)
*Note both groups have same expression (x-3) left after taking out the common factor and that ensures the factoring is correct.
4) Lastly, combine the common factors extracted from each group
Final answer: (x^2+2)(x-3)
* Note you do not write (x-3) twice since is the same.
What is common factor?
Factors that are common to two or more numbers are said to be common factors.
Citation (image):
- http://misscalculate.blogspot.com/2011/12/factoring-ax2-bx-c.html
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