How do you factor #x^2 - 4x - 12#?

1 Answer
Don't Memorise
Nov 17, 2015

#x^2 - 4x - 12=color(green)((x-6)(x+2)#

Explanation:

#color(red)(x^2 - 4x - 12#

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 = -4#

After trying out a few numbers we get #N_1 = -6# and #N_2 =2#

#-6*2 = -12#, and #-6+(2)= -4#

#color(red)(x^2 - 4x - 12) = x^2 - 6x + 2x - 12#

# = x(x-6) + 2(x-6)#

#(x-6)# is a common factor to each of the terms

#=color(green)((x-6)(x+2)#

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