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

1 Answer
David B.
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)#

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