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

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Answer 1 · 2015-12-18T14:22:12

#y = 3x(x^2 - 100)#

There is at least one #x# on every term at the right so you can already factorize by #x#, which gives you #y = x(3x^2 + 300)#.

But 300 and 3 both have 3 as common divisor, so you can also say that #y = 3x(x^2 - 100)#. I hope that answers your question.

Answer 2 · 2015-12-18T16:18:39

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

Factoring out #3x# gives:

#y=3x(x^2-100)#

But #100# is #10^2# giving:

#y=3x(x^2-10^2)#

Known: #(a^2-b^2)=(a-b)(a+b)#

Applying this to our question gives:

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