factor 5x cubed minus 45x

Start with: 5x^{3} - 45x.

You can factor out every term starting with constants; in this case 5.

5 ( x^{3} - 9x)

Next step, factor out the x so

5x (x^{2} - 9)

Using FOIL, you can then factor out the term in the parenthesis (x^{2} - 9). Note there is no x term and the 9 is a perfect square. You get (x -3) (x + 3).

So, in its final form you get

(5x )(x - 3) (x + 3)

which can also be written as

5(x)(x-3)(x+3)