How do you write 3y²-16y-12 in factored form?

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Answer 1 · 2015-09-19T15:33:06

#color(green)((3y+2) (y -6) # is the factorised form.

#3y^2-16y-12#

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 = 3*-12 = -36#
and
#N_1 +N_2 = b = -16#

After trying out a few numbers we get #N_1 = -18# and #N_2 =2#
#-18*2 = -36#, and #-18+(2)= -16#

#3y^2-16y-12 =3y^2-18y +2y-12#

#= 3y(y -6) +2 (y-6)#

#color(green)((3y+2) (y -6) # is the factorised form.