How do you factor #6x^2+7x+2#?

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Answer 1 · 2015-05-04T08:50:23

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 = 6*2 = 12#
AND
#N_1 +N_2 = b = 7#

After trying out a few numbers we get #N_1 = 3# and #N_2 =4#

#3*4 = 12#, and #3+4= 7#

#6x^2 + 7x + 2 = 6x^2 +3x + 4x + 2#

# = 3x(2x+1) + 2(2x+1)#

#2x+1# is a common factor to each of the terms

#=color(green)((2x+1)(3x+2)#