Question

How do you factor `12x²-24x+9`?

Answer 1

`12x^2-24x+9 = 3(2x-1)(2x-3)`

Explanation:

First separate out the common scalar factor `3`:

`12x^2-24x+9 = 3(4x^2-8x+3)`

To factor the remaining quadratic `4x^2-8x+3` use an AC method:

Find a pair of factors of `AC = 4*3=12` with sum `B=8`

The pair `6, 2` works.

Use this pair to split the middle term and factor by grouping:

`4x^2-8x+3 = 4x^2-6x-2x+3`

`color(white)(4x^2-8x+3) = (4x^2-6x)-(2x-3)`

`color(white)(4x^2-8x+3) = 2x(2x-3)-1(2x-3)`

`color(white)(4x^2-8x+3) = (2x-1)(2x-3)`

Putting it all together:

`12x^2-24x+9 = 3(2x-1)(2x-3)`