Factor 2x2-5x plus 12

2x^(2) - 5x - 12

First write down all the factors of '2' & '12'

2 = 1,2

12 = 1,12; 2,6; 3,4 .

From this we select two pairs of numbers, one pair from each coefficient, that add/multiply to '5'

They are, 1,2 & 3,4

Hence

-(2 x 4) + (1 x 3) = -8 + 3 = -5

Set up the brackets

(2x 3)(x 4)

Hence the signs are

( 2x + 3)(x - 4)