5. а) Factor the polynomial f (x) = 3xª+2x³+2x² +2x-1 into irreducible polynomials in C[r], R[7), and Q[r).

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Chapter2: Second-order Linear Odes
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5. а)
Factor the polynomial f (x) = 3x4+2x³ +2x²+2x-1 into irreducible polynomials
in C[a], R[x], and Q[z).
b)
Check if f (x) = 4x5 + 3xª – 12x² +3 is irreducible in Q[x].
c)
Check if f (x) = x* + 7x³ + 14x² + 3 is irreducible in Q[x].
Transcribed Image Text:5. а) Factor the polynomial f (x) = 3x4+2x³ +2x²+2x-1 into irreducible polynomials in C[a], R[x], and Q[z). b) Check if f (x) = 4x5 + 3xª – 12x² +3 is irreducible in Q[x]. c) Check if f (x) = x* + 7x³ + 14x² + 3 is irreducible in Q[x].
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