How do you factor #12d^2 + 4d - 1#?

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Answer 1 · 2015-09-23T12:47:02

#color(blue)((2d+1) (6d -1 ) # is the factorised form of the expression.

#12d^2 +4d -1#

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

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

#N_1*N_2 = a*c = 12*-1 = -12#
AND
#N_1 +N_2 = b = 4#

After trying out a few numbers we get #N_1 = -6# and #N_2 =2#
#(-2)*6 = -12#, and #6+(-2)= 4#

#12d^2 +color(blue)(4d) -1 = 12d^2 color(blue)(-2d +6d) -1#

#=2d (6d -1 ) +1(6d -1)#

#color(blue)((2d+1) (6d -1 ) # is the factorised form of the expression.