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Linear Factorization Theorem Proof
SOLVED: 14. In each part, explain why [f(x)] is a unit in F[x]/(p(x)) and find its inverse. [Hint: To find the inverse, let u(x) and v(x) be as in the proof of Theorem 5.9. You may assume that u(x) = ax b and v(x) = e d. Expanding f(x)(u(x) p(x)v(x)) leads to a system of linear equations in a, b, e, and d. Solve it.] (a) [f(x)] = [2x^3] / (x^2 - 2)(b) [f(x)] = [x 1] / (x 1)
SOLVED: 14. In each part, explain why [f(x)] is a unit in F[x]/(p(x)) and find its inverse. [Hint: To find the inverse, let u(x) and v(x) be as in the proof of Theorem 5.9. You may assume that u(x) = ax b and v(x) = e d. Expanding f(x)(u(x) p(x)v(x)) leads to a system of linear equations in a, b, e, and d. Solve it.] (a) [f(x)] = [2x^3] / (x^2 - 2)(b) [f(x)] = [x 1] / (x 1)
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Use the linear factorization theorem to find polynomials with given zeros
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