Question

How do you factor `5x^3-45x`?

Answer 1

`5x^3-45x = 5x(x-3)(x+3)`

Explanation:

To factor this expression, we must be able to factor each part of it. Then we look for common things, and pull them out. We can write our expression as a set of factors for each term as:

`color(blue)(5x^3)-color(red)(45x) = color(blue)(5*x*x*x)-color(red)(5*3*3*x)`

We can see that each term has a factor of `color(magenta)(5)` and `color(magenta)(x)` in common, so we can "pull those out"

`color(magenta)(5x)(color(blue)(x*x)-color(red)(3*3))`

Finally, we can try to factor the expression further noticing that it is the difference of squares:

`5x^3-45x = 5x(x-3)(x+3)`