The zeroes are the roots when f(x)=0. So x^2-x-12 needs to be factorised so that we can find the roots. We're looking for two integers whose product is 12 and whose difference is 1. The factors of 12 are 1 and 12, 2 and 6, and 4 and 3. The last pair fit the requirements because 4-3=1 and 4*3=12. The factors are therefore (x 3) and (x 4) and the sign between is either + in the first bracket and - in the second or vice versa. The minus sign needs to be in front of the larger number because we have -x in the equation, so the factors are (x+3)(x-4) and if this is equal to zero, x+3=0 or x-4=0, making the roots and zeroes -3 and 4.