How do you factor #12y^2-7y+1 #?

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Answer 1 · 2015-08-11T16:42:25

#color(blue)((3y-1)(4y-1) # is the factorised form of the expression.

#12y^2−7y+1 #

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

In this technique, if we have to factorise an expression like #ay^2 + by + 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 = -7#

After trying out a few numbers we get #N_1 = -3# and #N_2 =-4#
#-3*-4 = 12#, and #-3+(-4)= -7#

#12y^2−color(blue)(7y)+1 =12y^2−color(blue)(3y -4y)+1 #

#= 3y(4y-1) -1(4y-1) #
#color(blue)((3y-1)(4y-1) # is the factorised form of the expression.