How do you factor the trinomial #3x^2+2x-1=0#?

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Answer 1 · 2016-03-01T18:35:58

# (3x-1) (x+1) # is the factorised form of the expression.

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

AND

#N_1 +N_2 = b = 2#

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

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

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

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

# (3x-1) (x+1) # is the factorised form of the expression.