problem: Robert is doing his quadratics factoring worksheet when a drop of ink ruins part of his work.
  
  The problem asks him to factor $-35-x+12 x^2$ and he has correctly figured out one of two factors: $(3x + 5).$ What must be the other factor?
solution: Given that we have $- 35 - x + 12x^2$ and the factor $3x + 5$, we can guess that the other factor must be $4x - 7$ since the linear terms must multiply to $12x^2$ and the constant terms must multiply to $-35.$
  
  Expanding, we can verify that this is correct, and therefore our answer is $\boxed{(4x - 7)}.$