(4x + 1)(x - 5)
to start, we know that we will get something in the form of (ax + b)(cx + d), or (ac)x^2 + (ad + bc)x + bd. making some equations, we can see that ac = 4, ad + bc = -19, and bd = -5. notice that a and c cannot be 2 and 2, as 2d + 2b = -19 cannot be possible because -19 is odd. therefore, a is 4 and c is 1 (or vice versa). plug this back in to get 4d + b = -19, and bd = -5. simple guess and check shows that d = -5 and b = 1, so the answer is (4x + 1)(x - 5).