SOLUTION: I need to factor the following problem: 6x^2 - 13x + 6 It is not making sense to me at all. 6x(x-____+ 1) ??? Is this the start?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need to factor the following problem: 6x^2 - 13x + 6 It is not making sense to me at all. 6x(x-____+ 1) ??? Is this the start?      Log On


   



Question 370847: I need to factor the following problem: 6x^2 - 13x + 6
It is not making sense to me at all.
6x(x-____+ 1) ??? Is this the start?

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

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