The sign of the constant term (-12) is negative. That means it has one positive and one negative factor.
The algebraic sum of those factors of -12 must be -4. That means you are looking for two factors of 12 that differ by 4.
12 = 1*12 = 2*6 = 3*4 (these are the ways to factor 12 using integers)
Only the pair {2, 6} differ by 4. Now, figure which one of these must have the negative sign so that their sum is -4. (That would be -6, +2.)
It can help to rewrite the expression using your knowledge of how the -4y term is composed.
Y^2 - 4y - 12
= y^2 - 6y + 2y - 12 (here, we have rewritten -4 as -6+2)
= y(y-6) + 2(y-6) (we have factored the first pair of terms, and the last pair of terms)
= (y+2)(y-6) (we have factored out the common factor y-6 from the previous step)
The algebraic sum of those factors of -12 must be -4. That means you are looking for two factors of 12 that differ by 4.
12 = 1*12 = 2*6 = 3*4 (these are the ways to factor 12 using integers)
Only the pair {2, 6} differ by 4. Now, figure which one of these must have the negative sign so that their sum is -4. (That would be -6, +2.)
It can help to rewrite the expression using your knowledge of how the -4y term is composed.
Y^2 - 4y - 12
= y^2 - 6y + 2y - 12 (here, we have rewritten -4 as -6+2)
= y(y-6) + 2(y-6) (we have factored the first pair of terms, and the last pair of terms)
= (y+2)(y-6) (we have factored out the common factor y-6 from the previous step)
