Factoring

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Luke Luke
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Factoring

Hello, need help with this.
How to factor x^4+x^2+1 ?

Thanks.

Luke.
AlgebraHouse AlgebraHouse
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Re: Factoring

x^4 + x^2 + 1
= it does not factor

If you tried this:
(x² + 1)(x² + 1)
It would multiply to be x^4 + 2x^2 + 1 using the foil method
which would be incorrect.

- Algebra House
Luke Luke
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Re: Factoring

Factoring x^4+x^2+1
Hi,  as a matter of fact, it does factor, when I factor it with my TI 89 calculator, it gives the following result:
(x^2+x+1) (x^2-x+1) but I don't know  how to get this this doing it myself.
Greetings.
Luke.
AlgebraHouse AlgebraHouse
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Re: Factoring

You're right.  Most people are asking to see it simply factored into two binomials.
This is more of a College Algebra question.

Here's another look at it:

x^4 + x^2 + 1
= (x^4 + 2x^2 + 1) - x^2 {put 2x^2 inside parentheses and -x^2 on the outside}
= (x^2 + 1)^2 - x^2 {wrote x^4 + 2x^2 + 1 as the square of x^2 + 1}

Now you have a difference of two squares:
(x^2 + 1)^2 - x^2
= [(x^2 + 1) + x][(x^2 + 1) - x] {factored the difference of two squares into two binomials}
= (x^2 + x + 1)(x^2 - x + 1) {took out parentheses within brackets}

- Algebra House
Luke Luke
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Re: Factoring

Thank you.
Luke.