Question

How do you factor completely: `2x^3 - 18x`?

Answer 1

`2x^3-18x = (2x)(x+3)(x-3)`

Explanation:

Given `2x^3-18x`

Remove the obvious common factor `(2x)`
`color(white)("XXXX")` `=(2x)(x^2-9)`

Recognize the second term as the difference of squares
`color(white)("XXXX")` `=(2x)(x+3)(x-3)`
`color(white)("XXXX")` `color(white)("XXXX")` `color(white)("XXXX")`Since `(x^2-a^2) = (x+a)(x-a)`