Question

How do you factor `-12x^2+27`?

Answer 1

`-3(2x-3)(2x+3)`

Explanation:

Given
`color(white)("XXX")-12x^2+27`

we can remove the obvious integer factor `(-3)` to get
`color(white)("XXX")(-3)(4x^2-9)`

then recognizing `(4x^2-9)` as the difference of squares: `((2x)^2-(3)^2)`
with factors `(2x-3)` and `(2x+3)`

we obtain the result given above.