How do you factor #9z^2-12z+4#?

1 Answer
Don't Memorise
May 28, 2015

#9z^2-12z+4#

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like #az^2 + bz + c#, we need to think of 2 numbers such that:
#N_1*N_2 = a*c = 9*4 = 36#
and
#N_1 +N_2 = b = -12#
After trying out a few numbers we get #N_1 = -6# and #N_2 =-6#
#-6*(-6) = 36#, and #(-6)+(-6)= -12#

#9z^2-12z+4 = 9z^2-6z - 6z+4#

#=3z(3z - 2) -2(3z-2)#
#=color(green)((3z-2)(3z-2)#

note : We know that #color(green)((a - b)^2 = a^2- 2ab + b^2)#

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