Problem Solving

mustbeatgmat wrote:Hey guys,

I have a quick question about factoring and it doesnt seem to click with me in this particular circumstance. When given x^2-5x=0, i know to factor it --> x(x-5).

HOWEVER, when trying to factor out x^3-3x=0 --> it says to factor it out like this: x^2(x-3) BUT doesnt the x^2 get distributed to the 3 too and become 3x^2 instead of just 3x?

There must be a typo in the material you're working from, or you've mistranscribed the example. If you have x^3 - 3x, you cannot factor out x^2 (at least not without getting a fraction in the brackets). You can only factor out a single x:

x^3 - 3x = x(x^2 - 3)

If you needed to, you could factor further; the expression in brackets is a 'difference of squares'. That is, we can factor it using the familiar pattern a^2 - b^2 = (a+b)(a-b). So factoring completely:

x^3 - 3x = x(x^2 - 3) = (x)(x + sqrt(3))(x - sqrt(3))