Question

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

Answer 1

Yes. `y=(2x-3)^2`

Explanation:

If the general form of the factored quadratic is `y = (ax +b)(cx+d)` 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`.
`bc` and `ad` 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 `ac` and `bd` both give squares - `4` and `9` respectively.
The answer is therefore `(2x - 3)(2x -3)`
`=(2x-3)^2`