When factoring 3x^2 -26x + 35, why should both factors of c be negative

So you want to factor this polynom thus it will look like something like this
(x+a)(x+b) where a and b can be positive or negative 

now in our question the polynom ends with +35 that has no x in it. This part can only come from a*b. Two numbers multiplied can only be positive if they are both positive or if they are both negative. 
-26x this part comes from ax+bx part of the above equation. If both a and b are poitive than the result needs to be positive as well, this combining the two arguements we come to the conclusion that they are both negative.