Question

How do you factor `18x^3-6x^2+9x`?

Answer 1

`18x^3-6x^2+9x = color(green)(3x(6x^2-2x+3)`

Explanation:

Given
`color(white)("XXX")18x^3-6x^2+9x`

Extracting the (hopefully) obvious factor of `color(brown)(3x)`
`color(white)("XXX")=color(brown)(3x)(6x^2-2x+3)`

Checking the discriminant: `b^2-4ac`:
`color(white)("XXX")(-2)^2-4xx6xx3=-68 < 0`
`color(white)("XXX")rArr`no Real roots

`rArr 3x(6x^2-2x+3)` is the complete factorization (in `RR`).