factor 6x^2-17x+5?

6x^2 - 17x + 5 = 0
6x^2 - 15x - 2x + 5 = 0
3x (2x - 5) -1 (2x - 5) = 0
(3x - 1) (2x - 5) = 0
x = 1/3 or 5/2

6x^2 - 17x + 5
= 6x^2 - 2x - 15x + 5
= (6x^2 - 2x) - (15x - 5)
= 2x(3x - 1) - 5(3x - 1)
= (3x - 1)(2x - 5)

(3x - 1)(2x - 5)

it can be factored at (3x-1)(2x-5). You may check the answer by multiplying (FOIL) the answer (3x-1)(2x-5) = 6x^2 -15x -2x +5 = 6x^2 -17x +5