If P, be a polynomial of degree n, i.e., P, = aok" + a;k"-1. + a, then A" P. = aon!.

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A: A set S  is said to be countable if it has a one - to - one function as f:S→N.

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A: Note : As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: 6- Show that the Polynomial has a Z4 [x] 2X+1 in multiplicative invers. in 24 [x].

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A: The number of reducible monic polynomials of degree 2 over Z3 is

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A: Given: 2+i To find:  The irr(ꭤ,ℚ) and deg(ꭤ,ℚ)for the given algebraic number ꭤ ∈ ℂ.

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Q: 1. Use polynomial fitting to find a closed form for 5, 8, 13, 20, 29, ...

A: Given , Sequence = 5,8,13,20,29,.....   To find: Closed form of sequence i.e. formula for nth term .

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A: Answer is mentioned below

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Q: 32. If p(x) is a polynomial in Z,[x] with no multiple zeros, show that p(x) divides xP" . x for some…

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A: Answer

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Q: Number theory

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Q: Q) prove that (1) -2P xSinx 2.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 2. List all the polynomials in Z3[x] that have degree 2.

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Q: (1) For each member of your group record their response to: Give an example of a polynomial and an…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Suppose​ f(x) is a 7th degree polynomial. Using a few complete​ sentences, explain why we are…

A: Given f(x) is a 7th degree polynomial.  Recall: fundamental theorem of algebra:  If f(x) is a…

Q: If P, be a polynomial of degree n, i.e., P = agk" + a;k"-1 + a, then A" P = aon!. %3D

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Q: Show that If |z| = 1, then: -1 = Z

A: z is a complex number. z=a+ib |z|=(a+ib)(a-ib)     =a2-b2 if |z|=1, then a2+b2=1

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Q: Find the minimal polynomial satisfied by √2 + √5. over Q.

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Q: For n > 3, prove that the numbers ±5, ±52, · reduced residue system modulo 2". form a

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Q: 3. Prove that the sandwitch theorem.

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Q: 5. Show that there are infinitely many irreducible polynomials in F,[X].

A: By the method of contradiction i have solved the problem