Question

How to solve step by step the following polynomial factoring problem:

(x + 3) - x(x^{2} + 6x+9)

Answer 1

`(x+3)(1-x^2-3x)`

Explanation:

First, let's factor that quadratic on the right:

`x^2+6x+9` happens to factor nicely into
`(x+3)^2`, and putting that into our expression gets us

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

Factoring out an (x + 3) from each term, we get

`(x+3)[1-x(x+3)]`

Simplifying that expression on the right:

`(x+3)(1-x^2-3x)`

We can't factor that right-side expression any more, so we can just leave it like that!

Answer 2

(x + 3) - x(x² + 6x + 9)

= (x + 3) - x(x + 3)²

= (x + 3)[1 - x(x + 3)]

= (x + 3)(1 - x² - 3x)

Explanation: