How do you factor # x^3 - 9x = 0#?

1 Answer
Feb 20, 2016

Answer:

#x(x+3)(x-3)=0#

Explanation:

First, notice that the term #x# is common in both terms on the left hand side. Thus, it can be factored from the two.

#x(x^2-9)=0#

Now, we should consider the quadratic term #x^2-9#. This is actually a difference of squares, since both #x^2# and #9# are squared terms being subtracted: #x^2=(x)^2,9=(3)^2#.

Differences of squares factor as follows:

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

Hence in #x^2-9# we have #a=x# and #b=3#, so the original expression factors into:

#x(x+3)(x-3)=0#

This is completely factored.