Question

How do you write `(x^3 - x^2 - 6x)` in factored form?

Answer 1

`x(x^2-x-6)`
`x(x-3)(x+2)`

Explanation:

`x^3-x^2-6x`

1) Simplify the polynomial.
( What does each term have in common? )

In this case, they each have `1x` or `x` in common

2) Place the extraneous parts on the outside.
(Put what you just simplified outside the parentheses)

In this example, that means `x`
`x(x^2-x-6)`

3) Factor the trinomial.
(Just like you usually would)

I was taught to think of a number that multiplies to make the last number (`6`) and add together to make the middle coefficient (`1`). When you do that you get `-3` and `2`. So, the answer is:
`x(x-3)(x+2)`

Notes:
- You should always simplify before you begin factoring because it makes it easier and faster.
- You can always check you answer by multiplying the equation back out again. If you did it right, you should get what you started with