How do you factor #x^2 - x - 12?#?

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Answer 1 · 2015-05-03T07:33:27

We can Split the Middle Term of this expression to factorise it

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*-12 = -12#
AND
#N_1 +N_2 = b = -1#

After trying out a few numbers we get #N_1 = 3# and #N_2 =-4#

#3*-4 = -12#, and #3+(-4)= -1#

#x^2 - x - 12 = x^2 +3x - 4x - 12#

# = x(x+3) - 4(x+3)#

#x+3# is a common factor to each of the terms

#=color(green)((x+3)(x-4)#