How do you factor #x^2-x-42#?
We can Split the Middle Term of this expression to factorise it.
In this technique, if we have to factorise an expression like
After trying out a few numbers we get
Factor y = x^2 - x - 42.
Ans: (x + 6)(x - 7)
Using the new AC Method (Socratic Search) is simpler and faster.
y = x^2 - x - 42 = (x + p)(x + q).
p and q have opposite signs. Factor pairs of (-42) --> (-3, 14)(-6, 7). This sum is 1 = -b. The opposite sum gives p and q --> p = 6
and q = -7.
Factored form: y = (x + 6)(x - 7)
NOTE . This new AC Method shows a systematic way to find the 2 numbers p and q, instead of guessing. In addition, it avoids the lengthy factoring by grouping.