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

1 Answer
May 9, 2016

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)