How do you factor 9x^3-x?

3 Answers
Jan 25, 2017

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 ).

Jan 25, 2017

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

Explanation:

9x^3-x

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

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

Jan 25, 2017

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"