Here are the steps to using a t-table to complete the box when factoring ax2+bx+c.
The left column should be all of the factor pairs of ac.
If c is positive, the factors will have the same sign. If c is negative, the factors will have opposite signs. In both cases, the larger factor will have the same sign as b.
Find the factor pair whose sum is b. These factors will be what you use to fill the box. Remember to multiply by your variable. (For example, write 2, 3 as 2x and 3x...)