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flyers
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Homework Statement
I am trying to factor x4+1 into two multiplied polynomials
Homework Equations
My teacher gave us this hint that its factored form is (ax2+bx+c)(ax2+bx+c)
The Attempt at a Solution
First i assumed that a and c were equal to 1 so that when x2 is multiplied by the other x2 is gives me x4 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.)
(x2+ax+1)(x2-bx+1)= x4+1
and I get
x4+ax3-bx3+2x2-abx2+ax-bx+1= x4+1 canceling terms I get
ax3-bx3+2x2-abx2+ax-bx=0
I noticed that to cancel out ax3-bx3 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=b2
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.