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

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

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Answer 1 · 2015-05-28T15:34:07

$9z^2-12z+4$

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

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