How do you factor #12x^2+7x-5#?

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Answer 1 · 2015-09-20T16:52:14

#color(blue)((12x-5)(x+1)# is the factorised form.

#12x^2 +7x -5#

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 = 12*-5 = -60#

and

#N_1 +N_2 = b = 7#

After trying out a few numbers we get #N_1 = 12# and #N_2 =-5#
#12*-5 = -60 #, and #12+(-5)= 7#

#12x^2 +7x -5 =12x^2 +12x - 5x -5#

#=12x(x+1) -5(x+1)#

#color(blue)((12x-5)(x+1)# is the factorised form.