How do you factor completely: #3x^2 + 2x − 1#?

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Answer 1 · 2015-07-24T13:34:10

#=color(blue)((3x-1)(x+1)#

#3x^2+2x−1#

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 = 3*-1 = -3#
and
#N_1 +N_2 = b = 2#

After trying out a few numbers we get:
#N_1 = 3# and #N_2 =-1#
#3*(-1) = -3#, and #3+(-1)=2 #

#3x^2+2x−1 =3x^2+3x -1x−1 #

#=3x(x+1) -1(x+1) #

#(x+1) #is common to both terms here:

#=color(blue)((3x-1)(x+1)#