Hi

5x^2 - 8x +3 = 0   |After factoring, the factors must represent the original

factoring to a product (__ -  __)(  -  __) Note:  -1*-3 = 3

 (5x -  __)(x  -  __)   |5x and x need to be in the 1st spots

 (5x -  __)(x  -  __)   | 3 and 1 need to go into one or the other of 2nd spot blanks

 (5x -3)(x-1)=0        |this arrangement works for placing the 3 and 1

 Noting: The SUM of the inner product(-3x) and the outer product(-5x) = -8x



CHECKING our Answer

 5x(x-1) - 3(x-1) = 5x^2 - 5x - 3x +3 = 5x^2 -8x +3

Hope this helps to clarify this

Another ex would be:

 x^2 -5x + 4   | -4*-1 = 4

(x - 4)(x - 1) |SUM of the inner product(-4x) and the outer product(-x) = -5x

 

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