Factoring question

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January 31st 2010, 01:05 PM
james121515

Factoring question

Hi,

What is the best method to go about factoring this $x^6+6x^4+10x^2+8$ ? Can this be done by grouping? I tried to do rational root tests but it appears as though it does not have any rational roots.

Thanks for your help,
James
January 31st 2010, 01:13 PM
pickslides

Quote:

Originally Posted by james121515

Hi,

What is the best method to go about factoring this $x^6+6x^4+10x^2+8$ ? Can this be done by grouping? I tried to do rational root tests but it appears as though it does not have any rational roots.

Thanks for your help,
James

Might be helpful to say $a = x^2$ making the whole thing cubic instead.
January 31st 2010, 01:16 PM
skeeter

Quote:

Originally Posted by james121515

Hi,

What is the best method to go about factoring this $x^6+6x^4+10x^2+8$ ? Can this be done by grouping? I tried to do rational root tests but it appears as though it does not have any rational roots.

Thanks for your help,
James

$y = x^6+6x^4+10x^2+8 > 0$ for all $x$ ... no real roots.
January 31st 2010, 01:17 PM
Henryt999

Well

Thats an expression you have no = sign anywhere.
Also it doesn´t have any x intercepts so it doesn´t factor.
January 31st 2010, 01:25 PM
james121515

It factors to $(x^2+2)^3$ . I'm curious as to what method you use to do it.
January 31st 2010, 01:33 PM
pickslides

Quote:

Originally Posted by james121515

It factors to $(x^2+2)^3$ . I'm curious as to what method you use to do it.

$x^6+6x^4+10x^2+8$

make $a = x^2$ now

$a^3+6a^2+10a+8$

Then employee the factor theorem checking positive and negative factors of 8.

Spoiler:

$a = -2$

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