Hi, I needed to factor x^4+5x^2+4. I understand the answer is (x-2)(x-1)(x+1)(x+2)

Can anyone tell me how to go about answering this though? How do I figure it out?

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- January 7th 2011, 08:39 PMfrankinaroundfactoring x^4+5x^2+4
Hi, I needed to factor x^4+5x^2+4. I understand the answer is (x-2)(x-1)(x+1)(x+2)

Can anyone tell me how to go about answering this though? How do I figure it out? - January 7th 2011, 08:43 PMdwsmith
let w^2=x^4

- January 7th 2011, 08:44 PMsnowtea
Are you sure it is not x^4 - 5x^2 + 4?

Substitute y = x^2 to get y^2 - 5y + 4.

First factor this, then resubstitue in x^2 and continue factoring. - January 7th 2011, 08:44 PMProve It
In other words, let .

- January 7th 2011, 08:46 PMRandom Variable
If all else fails, search for a root and then use synthetic division.

- January 7th 2011, 08:49 PMProve It
- January 7th 2011, 09:01 PMTheCoffeeMachine
Or complete the square:

.

Of course you know that . - January 7th 2011, 09:01 PMRandom Variable
- January 8th 2011, 05:22 AMArchie Meade
- January 10th 2011, 05:55 PMfrankinaround
thanks everyone. That substitution is great, but in the future how can I know to use that kind of substitution? meaning what if it was a little bit different right? then how would you solve it? or how did you know to substitute y=x^2 ? The quadratic equation didnt work for x^4 thats why im asking. So does that mean you just need to find any way to make it ax^2+bx+c?

- January 10th 2011, 07:02 PMmr fantastic