# Rearranging negative polynomials

• Jan 18th 2013, 09:56 PM
zsf1990
Rearranging negative polynomials
Given 6 + 2x + 3x3 - x4, how would I rearrange it into descending order to be factored? I know addition is commutative, but given that x4 is negative, how do I move that without changing the expression?
• Jan 18th 2013, 11:22 PM
chiro
Re: Rearranging negative polynomials
Hey zsf1990.

Try using:

6 + 2x + 3x^3 - x^4 = - (x^4 - 3x^3 - 2x - 6)
• Jan 19th 2013, 03:07 PM
zsf1990
Re: Rearranging negative polynomials
Thanks! Any chance you could explain how to factor 5x3 - 40? -40 isn't a perfect cube, so I'm feeling lost. This is what I get for missing a lecture I guess.

EDIT: Nevermind. Factor out a five to get x3 - 8, which is a difference of cubes. It's always the little things, lol.
• Jan 19th 2013, 03:09 PM
Plato
Re: Rearranging negative polynomials
Quote:

Originally Posted by zsf1990
Thanks! Any chance you could explain how to factor 5x3 - 40? -40 isn't a perfect cube, so I'm feeling lost. This is what I get for missing a lecture I guess.

EDIT: Nevermind. Factor out a five to get x3 - 8, which is a difference of cubes. It's always the little things, lol.

You have a typo in the question,
• Jan 19th 2013, 03:10 PM
zsf1990
Re: Rearranging negative polynomials
I'm not sure I'm following. The question mark is a typo?
• Jan 19th 2013, 03:17 PM
Plato
Re: Rearranging negative polynomials
Quote:

Originally Posted by Plato
You have a typo in the question,

Did you want to factor $5x^3-40~?$

You seemed to say factor $5x^3-40?-40$
• Jan 19th 2013, 03:25 PM
zsf1990
Re: Rearranging negative polynomials
Ah. My bad. It was factor 5x[sup]3 - 40.

As I move on with my homework, what are the steps to factoring this polynomial? 5(3-4x)2 - 8(3-4x) (5x-1) I'm not sure where to start.
• Jan 19th 2013, 03:25 PM
Prove It
Re: Rearranging negative polynomials
Quote:

Originally Posted by Plato
Did you want to factor $5x^3-40~?$

You seemed to say factor $5x^3-40?-40$

No, the OP asked how to factor \displaystyle \begin{align*} 5x^3 - 40 \end{align*} and then went on to say in the next sentence that -40 is not a perfect cube.