How do you factor #x^2 - 2x - 8#?

1 Answer
Jun 10, 2015

Answer:

#color(blue)((x+2)(x - 4) #

Explanation:

#x^2 - 2x - 8#

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*(-8) = -8#
and
#N_1 +N_2 = b = -2#

After trying out a few numbers we get #N_1 = -4# and #N_2 =2#
#-4*2 = -8#, and #2+(-4)= -2#

#x^2 - 2x - 8 = x^2 - 4x +2x - 8#
#=x(x - 4) +2(x - 4)#
#=color(blue)((x+2)(x - 4) #