# Factoring Problem

• Nov 10th 2012, 03:45 PM
Jason76
Factoring Problem
How does

\$\displaystyle 1 - 9x^{2} + 24x^{4} - 16x^{6}\$

become

\$\displaystyle (1 - x^{2})(16x^{4} - 8x^{2} + 1)\$ ?
• Nov 10th 2012, 04:02 PM
Plato
Re: Factoring Problem
Quote:

Originally Posted by Jason76
How does
\$\displaystyle 1 - 9x^{2} + 24x^{4} - 16x^{6}\$
become
\$\displaystyle (1 - x^{2})(16x^{4} - 8x^{2} + 1)\$ ?

@Jason76, you are basically lazy are you not?

You demand to know "How does...become"?

Are you to lazy to multiply \$\displaystyle (1 - x^{2})(16x^{4} - 8x^{2} + 1)\$ out to see how it all works?
• Nov 10th 2012, 04:04 PM
chiro
Re: Factoring Problem
Hey Jason76.

You might want to look at this:

Rational root theorem - Wikipedia, the free encyclopedia
• Nov 10th 2012, 04:34 PM
Jason76
Re: Factoring Problem
\$\displaystyle 1 - 9x^{2} + 24x^{4} - 16x^{6}\$

Pulling out x^{2}

\$\displaystyle 1 - [x^{2}(9 + 24x^{2} - 16x^{4})]\$

\$\displaystyle (1 - x^{2})(9 + 24x^{2} - 16x^{4})\$

After that, nothing in the right linear has any common factor, so you can't do anymore. But that's not the final answer.
• Nov 10th 2012, 04:55 PM
Plato
Re: Factoring Problem
Quote:

Originally Posted by Jason76
\$\displaystyle 1 - 9x^{2} + 24x^{4} - 16x^{6}\$

Pulling out x^{2}

\$\displaystyle 1 - [x^{2}(9 + 24x^{2} - 16x^{4})]\$

\$\displaystyle (1 - x^{2})(9 + 24x^{2} - 16x^{4})\$

After that, nothing in the right linear has any common factor, so you can't do anymore. But that's not the final answer.

You did nothing about replay #2.
Are you really that lazy?
• Nov 10th 2012, 05:03 PM
Jason76
Re: Factoring Problem
Quote:

Originally Posted by Plato
You did nothing about replay #2.
Are you really that lazy?

You can't do anymore cause there are no more common factors from what I see. 9, 24, and 16 have no common factor.
• Nov 10th 2012, 05:17 PM
Plato
Re: Factoring Problem
Quote:

Originally Posted by Jason76
You can't do anymore cause there are no more common factors from what I see. 9, 24, and 16 have no common factor.

If you do not have a complete understanding of how multiplication works, then you cannot understand factoring.
• Nov 11th 2012, 02:32 AM
Petrus
Re: Factoring Problem
Quote:

Originally Posted by Jason76
How does

\$\displaystyle 1 - 9x^{2} + 24x^{4} - 16x^{6}\$

become

\$\displaystyle (1 - x^{2})(16x^{4} - 8x^{2} + 1)\$ ?

Hello Jason!
First you use rational root theorem to find roots then you will use long polynom division to divide the root out.