Question

How do you factor `9x^3-x`?

Answer 1

`x ( 3x + 1 )( 3x-1 )`

Explanation:

`x` is common to both terms, so you can take it out of both and put the other factor in a bracket.

`9x^3 -x =x ( 9x^2 - 1)`.

`(x^2 -1)` and similar expressions are known as the difference of two squares, and can be further factorised to give:

`x( 3x + 1 )( 3x - 1 )`.

Answer 2

`x(3x-1)(3x+1)`

Explanation:

`9x^3-x`

`:.=x(9x^2-1)`

`:.=x(3x-1)(3x+1)`

Answer 3

`x(3x-1)(3x+1)`

Explanation:

There is a `color(blue)"common factor"` of x in both terms.

`rArrx(9x^2-1)larrcolor(red)"remove common factor"`

`9x^2-1" is a"color(blue)" difference of squares"` and factorises, in general as shown.

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^2-b^2=(a-b)(a+b))color(white)(2/2)|)))`

`"here " (3x)^2=9x^2" and " 1^2=1`

`rArra=3x" and " b=1`

`rArr9x^2-1=(3x-1)(3x+1)`

`rArr9x^3-1=x(3x-1)(3x+1)larrcolor(red)" fully factorised"`