You can put this solution on YOUR website! 3x² - 17x +10 =(3x-2)(x-5)
This is fairly easy to see. If a trinomial is factorable into two binomials, and the coefficient of the x^2 is a prime, one factor has to have that as its x coefficient. The other binomial's x coefficient will be 1. Then, all we need to do is find what adds to get -17 (including the 3 coefficient) and multiplies to get 10.