Question

How do you factor completely `5x^3 - 45x`?

Answer 1

`5x^3-45x = 5x(x-3)(x+3)`

Explanation:

Notice that both of the terms are divisible by `5x`, so we can separate that out as a factor first, then use the difference of squares identity:

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

with `a=x` and `b=3` as follows:

`5x^3-45x = 5x(x^2-9) = 5x(x^2-3^2) = 5x(x-3)(x+3)`