# Thread: Factoring question

1. ## Factoring question

Hi,

What is the best method to go about factoring this $\displaystyle x^6+6x^4+10x^2+8$? 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

2. Originally Posted by james121515
Hi,

What is the best method to go about factoring this $\displaystyle x^6+6x^4+10x^2+8$? 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 $\displaystyle a = x^2$ making the whole thing cubic instead.

3. Originally Posted by james121515
Hi,

What is the best method to go about factoring this $\displaystyle x^6+6x^4+10x^2+8$? 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
$\displaystyle y = x^6+6x^4+10x^2+8 > 0$ for all $\displaystyle x$ ... no real roots.

4. ## Well

Thats an expression you have no = sign anywhere.
Also it doesn´t have any x intercepts so it doesn´t factor.

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

6. Originally Posted by james121515
It factors to $\displaystyle (x^2+2)^3$. I'm curious as to what method you use to do it.
$\displaystyle x^6+6x^4+10x^2+8$

make $\displaystyle a = x^2$ now

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

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

Spoiler:
$\displaystyle a = -2$