Hi,

factor the following problem: 

6x^2 - 13x + 6 

factoring will result in 2 products:

(?x - ?)(?x - ?)  Asking ourselves what 2 numbers have a product of 6? 

Both 2*3 and 6*1 could work for this trinomial for the coefficient of x^2 and the constant.

Trying various combinations to complete the factoring

(3x - ?)(2x - ?)  

We NEED the 'sum of the inner and outer products' to match the middle term -13x.

(3x - 2)(2x - 3)this arrangement works as: 

SUM of the outer product(-9x)  and the inner product(-4x) = -13x



checking our answer

(3x - 2)(2x - 3) = 3x(2x-3) -2(2x-3) = 6x^2 -9x -4x +6 = 6x^2 -13x + 6

 

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