Given x2 + X + 1 = 0, find X4 + 1 / X4

x²+1=-x
Square on both sides
x⁴+2x²+1=x²
x⁴+1=-x²
Square on both sides
x^8+2x⁴+1=x⁴
x^8+1=-x⁴
Divide both sides by X & # 8308;
x⁴+1/x⁴=-1

Decomposition factor: x4-x3 + 4x2 + 3x + 5

x4-x3+4x2+3x+5=（x4+x3+x2）-（2x3+2x2+2x）+（5x2+5x+5）=x2（x2+x+1）-2x（x2+x+1）+5（x2+x+1）=（x2-2x+5）（x2+x+1）．

Decomposition factor: x4-4x2 + 3 =?

Original = (X & # 178; - 1) (X & # 178; - 3)
=(x+1)(x-1)(x²-3)

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