Is it possible to factor y= 4x^2 -12x + 9 ? If so, what are the factors?

Jan 15, 2016

Yes. $y = {\left(2 x - 3\right)}^{2}$

Explanation:

If the general form of the factored quadratic is $y = \left(a x + b\right) \left(c x + d\right)$ then
y = acx^2 + (bc+ad)x +bd)

This means that we need factors $a$ and $c$ that multiply to give $4$ and $b$ and $d$ that multiply to give $9$.
$b c$ and $a d$ must add up to give $- 12$

Because the sign of the middle term is negative and the sign of the last term is positive, both $b$ and $d$ must be negative.
In this example $a c$ and $b d$ both give squares - $4$ and $9$ respectively.
The answer is therefore $\left(2 x - 3\right) \left(2 x - 3\right)$
$= {\left(2 x - 3\right)}^{2}$