Factor X squared minus 2x minus 24

Ax^2+bx+c. To factor you are looking for two values, j and k, which satisfy to conditions:

ac=jk and b=j+k. We have:

x^2-2x-24 so in this case j=-6 and k=4

Now you replace the single linear term (the bx one) with two linear terms (jx and kx) into the original expression:

x^2-6x+4x-24 now you can factor the first and second pair of terms ...

x (x-6) + 4 (x-6) which is equal to:

(x+4) (x-6)