What multiplies to negative 140 and adds to negative 31?

If 2 numbers multiply to give you -140 then one of the numbers must be negative.  Let's just say x is negative.  If that's the case, then -xy = -140.  And if those same 2 numbers add to give -31, then -x + y = -31.  Solve the second equation for y to get y = x - 31. Sub in that y value into the first equation to get -x(x - 31) = -140.  Distributing and then changing all the signs to avoid a negative leading coefficient gives you the quadratic which factors nicely into x = 4 and x = -35.  Our x value has to be the positive one because we determined that x is negative (negative of a negative gives you a positive) so the x value is 4.  If you sub that into x in the first equation, you get -4y = -140 and y = 35.  So there you go!