The simplest technique for factoring is when one of the factors is a constant. When you do this, here are some rules to follow, which apply whenever the original polynomial has only rational coefficients (otherwise it gets more complicated):

- There can only be one constant factor, which comes first.
- In each non-constant factor, the leading coefficient should be positive.
- In each non-constant factor, all of the coefficients should be integers.
- In each non-constant factor, the coefficients should not have any common integer factor greater than 1.

- 6
*x*− 12 = 2(*x*− 2)3; - 6
*x*− 12 = −6(−*x*+ 2); - 6
*x*− 12 = 12(½*x*− 1); - 6
*x*− 12 = 2(3*x*− 6).

Here are some more examples:

- Look for a factor common to each term:
2
*y*+ 20 = 2 ⋅*y*+ 2 ⋅ 10 = 2(*y*+ 10). - Sometimes it helps to factor the coefficients:
6
*t*+ 15 = 2 ⋅ 3 ⋅ t + 3 ⋅ 5 = 3(2*t*+ 5). - You can also try to factor out a variable that appears in every term:
5
*x*^{3}+ 3*x*^{2}= 5*x**x**x*+ 3*x**x*=*x*^{2}(5*x*+ 3). - A negative coefficient on the leading term
means that a minus sign appears out front:
8 − 2
*x*= −2*x*+ 8 = −2*x*− −8 = −2(*x*− 4). - If the coefficients are fractional,
then their common denominator appears in the denominator out front:
½
*x*+ ⅔ = 3/6 ⋅*x*+ 4/6 = ⅙(3*x*+ 4).

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