How do you factor the trinomial #3m ^2 + 8m -3#?

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Answer 1 · 2016-04-06T12:50:27

#color(purple)((3m - 1) ( m + 3 )# is the factorised form of the expression.

#3m^2 + 8m - 3#

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

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

#N_1*N_2 = a*c = 3*(-3) = -9#

AND

#N_1 +N_2 = b = 8#

After trying out a few numbers we get #N_1 = 9# and #N_2 =-1#
#9*(-1) = -9#, and #9+(-1)= 8#

#3m^2 + 8m - 3 =3m^2 + 9m - 1m - 3 #

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

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

#color(purple)((3m - 1) ( m + 3 )# is the factorised form of the expression.