Question

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

Answer 1

`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.