The answer (9x +4)(x-8) is the correct set of factors for the starting polynomial while the (x+4/9) factor does not work. If you expand (using FOIL) the correct factors you get 9x^2 +4x-72x-32. Collecting the x terms gives you -68x so the final expansion is 9x^2 -68x-32 as required. The secret is to find the factors of 9 and 32 that when multipled and added together will give you -68. 9 factors to 3*3 or 9*1 and 32 factors to 16*2 or 4*8. Since you need 68 in the middle you need the large factors of 9, 1, 4 and 8. Since the sign of 32 is negative you know the signs for 4 and 8 are opposite. Since the sign for 68 is negative, you know the largest product (72) must be negative and that means the sign for 8 is negative. If you are solving for roots where the graph crosses at zero, then 9x+4=0 and x = -4/9. The other root is found from x-8 = 0 and x=8.