Q14E ... [FREE SOLUTION]

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Chapter 4: Q14E (page 119)

Short Answer

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It is proved that $f (x)$ is irreducible in $ℚ [x]$ .

Step by step solution

Step-by-Step Solution Step 1: Eisenstein’s Criterion

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Most popular questions from this chapter

(a) If f(x)and g(x) are associates in F[x], show that they have the same roots in F.

(b) If $f (x), g (x) \in F [x]$ have the same roots in F, are they associates in F[x] ?

If R is commutative, show that R[x] is also commutative.

Show that each polynomial $f (x)$ is irreducible in $ℚ [x]$ by finding a prime $p$ such that $f (x)$ is irreducible in $ℤ_{p} [x]$

(a) $7 x^{3} + 6 x^{2} + 4 x + 6$

Use unique factorization to find the gcd in $ℂ [x]$ of ${(x - 3)}^{3} {(x - 4)}^{4} {(x - i)}^{2}$ and $(x - 1) (x - 3) {(x - 4)}^{3}$ .

Find a prime p > 5such that x²+ 1is reducible in $ℤ_{p} [x]$ .

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Short Answer

Step by step solution

Step-by-Step Solution Step 1: Eisenstein’s Criterion

Prove the result

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Most popular questions from this chapter

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