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

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Answer 1 · 2015-12-03T07:59:27

#color(blue)((2x+1)(x+1)#

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

AND

#N_1 +N_2 = b = 3#

After trying out a few numbers we get:

#N_1 = 2# and #N_2 =1#

#2*1 =2#, and #2+1= 3#

#2x^2+color(blue)(3x)+1 = 2x^2+color(blue)(2x+1x)+1 #

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

Here, #(x+1) #is common to both terms ,

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

So, the factorised form of the equation is :
#color(blue)((2x+1)(x+1)#