(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am trying to factor x^{4}+1 in to two multiplied polynomials

2. Relevant equations

My teacher gave us this hint that its factored form is (ax2+bx+c)(ax2+bx+c)

3. The attempt at a solution

First i assumed that a and c were equal to 1 so that when x^{2}is multiplied by the other x^{2}is gives me x^{4}and 1 times 1 gives me 1. I knew that b had to be a constant so I multiplied...

(however i didnt know if both b's were the same so i split them into a and b. I also knew one of the constants must be negative so that variables cancel out.)

(x^{2}+ax+1)(x^{2}-bx+1)= x^{4}+1

and I get

x^{4}+ax^{3}-bx^{3}+2x^{2}-abx^{2}+ax-bx+1= x^{4}+1 canceling terms I get

ax^{3}-bx^{3}+2x^{2}-abx^{2}+ax-bx=0

I noticed that to cancel out ax^{3}-bx^{3}and ax-bx , a and b must be equal to each other. This means 2x2-abx2 = 0

2=ab(but they are the same) 2=b^{2}

b=[tex]\sqrt{}2[/tex]

So i checked my answer and it works out, but I am wondering if there is a more systematic approach to solve this so that I don't have to assume as much as I did.

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# Homework Help: Factoring (X^4+1)

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