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> How do I show that the three polynomials $f\_1 = t^2 + x^2 - 2$, $f\_2 = tx - 1$, $f\_3 = t^3 + 5tx^3 + 1$ generate the unit ideal in $\mathbb{C}[t, x]$?
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Artin mentions two approaches: by showing that they have no common zeros, and also by writing $1$ by a linear combination of $f\_1$, $f\_2$, $f\_3$, with polynomial coefficients.