Question

How do you factor the trinomial `a^3 - 6a^2 - 27a`?

Answer 1

`a(a+3)(a-9)`

Explanation:

To factor any sort of polynomial, you want to look for any common factors. This could be a common factor of a variable or a constant in every term.

In the polynomial `a^3-6a^2-27a`, you can easily recognize the common `a` in every term. To factor out the `a`, divide every term by the `a`.
Doing so gives you:
`a(a^2-6a-27)`

Now, all you have to worry about is the `a^2-6a-27`. Looking at factors of `-27` that add up to `-6`, hopefully you can recognize `3` and `-9`.

Now you have all your factors:

`a(a^2-6a-27) = a(a+3)(a-9)`
or
`a^3-6a^2-27a = a(a+3)(a-9)`