How do you factor the trinomial #12m^2+20m+3#?

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Answer 1 · 2015-12-07T12:44:46

#12m^2+20m+3 = color(green)((2m+3)(6m+1)#

We can Split the Middle Term of this expression to factorize it.

In this technique, if we have to factorize an expression like #am^2 + bm + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 12*3 = 36#

and

#N_1 +N_2 = b = 20#

After trying out a few numbers we get #N_1 = 18# and #N_2 =2#
#18*2 = 36#, and #18+2= 20#

#12m^2+20m+3 = 12m^2 +18m + 2m + 3#

# = 6m(2m + 3) + 1(2m + 3)#

#(2m+3)# is a common factor to each of the terms

#=color(green)((2m+3)(6m+1)#