How do you factor #3x^3-300x#?

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Answer 1 · 2015-05-18T01:51:57

First, let's factor out what both elements share: #3x#

#3x(x^2-100)#

Now, we can factor the quadratic inside the parenthesis by finding its roots and then turning them into factors:

#x^2=100#
#x=sqrt(100)#
#x=+-10#

#x=10# can be rewritten as #x-10=0#
#x=-10# can be rewritten as #x+10=0#

So, rewriting our factors, we have

#3x(x-10)(x+10)#