How do you factor the expressions #x^2+3x-4#?

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Answer 1 · 2016-03-03T18:06:50

#color(green)((x-1) (x+4) # is the factorised form of the expression.

#x^2 +3x -4#

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*-4 = -4#

AND

#N_1 +N_2 = b = 3#

After trying out a few numbers we get #N_1 = -1# and #N_2 =4#
#-1*4 = -4#, and #4+(-1)= 3#

#x^2 +3x -4 = x^2 +4x -1x-4#

#=x(x+4) - 1(x+4)#

#(x+4)# is a common factor to each of the terms
#=(x-1) (x+4) #

#color(green)((x-1) (x+4) # is the factorised form of the expression.