How do you factor #x^2 = x + 2 #?

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Answer 1 · 2016-03-23T17:42:51

#color(green)( (x +1 ) ( x-2 ) # is the factorised form of the expression.

#x^2 = x+2#

#x^2 - x -2 = 0#

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*(-2) = -2#

AND

#N_1 +N_2 = b = -1#

After trying out a few numbers we get #N_1 = -2# and #N_2 =1#
#1*(-2) = -2#, and #1+(-2)= -1 #

#x^2 - x -2 = x^2 - 2x + 1x -2 #

# = x ( x-2 ) + 1 (x-2)#

#(x-2)# is a common factor to each of the terms

# =color(green)( (x +1 ) ( x-2 ) #