Question 432574
It is somewhat tedious factoring such expressions with a relatively large leading coefficient, so we factor by finding the roots of the polynomial. If {{{9x^2 - 26x + 16 = 0}}}, then {{{x = (26 +- sqrt(676 - 4(9)(16)))/18 = (26 +- sqrt(100))/18 = (26 +- 10)/18}}} = 2 or 8/9. Hence our polynomial can be factored as {{{C(x-2)(x - 8/9)}}} where C is a constant. Since the leading coefficient ({{{x^2}}} term) is 45, then C = 45, so the polynomial is equal to {{{45(x-2)(x - 8/9)}}}. For sake of neatness, we can distribute the 9 into the {{{x - 8/9}}} to obtain integer coefficients: {{{5(x-2)(9x-8)}}}.