is the following fucntion analytic in mod(z)<2 and/or mod(z)>2. sqrt(z^(2)+2z+2)/ z^(2)-4z+3

Q: 6. What should be added from 2x +3x` -- x² -1, so that it becomes exactly divisible by (x-2)?

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Q: why are the polynomials x^4 + 2x^2 + x + 1 and x^4 + 1 are not irreducible over Z3 (mod3)

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Q: Find all n ∈ Z for which 3x^2 + 2nx + 12 is irreducible over Q.

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Q: The multiplicative inverse of x? + x in Z,[x]/ is: None X^4 X^3 X+1 O O O O

A: An element is inverse of another element means product of those two elements should be 1.

Q: Prove that for a # -1, a>0,n EN IS (1+a)^ n >=1+na.

A: Here let A=(1+a)n, a≠-1, a&gt;0, n∈N and B=1+na

Q: What is the exponent on the x variable of the 3st/nd/rd/th term in the expansion of 17 (x2 +3y)" ?…

A: using formula:-

Q: Determine whether x^5 + 2x^2 + 1 is reducible over Z13

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Q: Let & € N. Prove by using the contra-positive that if ³ is odd then is odd. Proof: Choose which of…

A: Introduction: The basis for proof by contra positive is the idea that an implication equals its…

Q: What is the coefficient of the term x^3y^2 expansion of (3x - y2)4?

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Q: 13. Let ZV2denote the set (a + V2|a, beZ}. Show that ZV2a subring of RSee Example 20.] 14. Let Tbe…

A: Test for the Subring: The non empty set S is subring of a ring R if  ∀a,b∈S a-b∈Sa·b∈S

Q: Find the negation of the quantified expression Vx³y(x² = 2^ y³ = 3) given the domain consists of…

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Q: If B' is of order 2x3 and BA is order 3x4, then A is of the order T

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Q: Show thet the Se nng + ベ+」 (+リ(2ペ+)+ ()) (ox) ナ (A+)(2p+1) (P+1) (28+1)(38+) (uhse a>0, B70) (uhse…

A: A series is said  to converge  if  the sequence of partial sums  converge. There are various tests…

Q: By considering uniqueness of factorization of integers, find all pairs (x, y) ∈ N^2 such that x^2 −…

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Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

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Q: 9. Show that 4x - 251 + 10x? – 15x + 20 is irreducible over Q.

A: Answer

Q: Solve the polynomial congruence x^3 - 3x^2 + 27 = 0 (mod 225). Please be detailed! I’m really…

A: Solution are fully explained in below steps Explanation:

Q: Which quantification proves a nonnegative number minus a negative number is positive? A Vxay(x 0) ^…

A: A ) ∀ x ∃ y(x&lt;y)

Q: Show, with justification, that (x^2+y^2)^2 =(x^2 -y^2)^2 +(2xy)^2   is an Identity.

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Q: x2 dx is (ax2+4)(x2+9)

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Q: What is the degree of the largest irreducible factor of (x^12)-1 over ℚ?   3 4 6 None of the above

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Q: R^n×n is invertible, show that AB is similar to BA for all B ∈ R^n×n.

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Q: rewrite the following complex numbers in z = x+ jy format

A: Since you have posted multipart question and we can answer three subparts. So, answered first three…

Q: What is the Coefficient o x' y b. 24 in (3x +y)? Plow monomials appear in +he meny expansion of (3x+…

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Q: state formally the Heine-Borel Theorem in R^k

A: Let S be a subset of ℝk. Then the Heine-Borel theorem states :

Q: Show that 3x^2 + 4x + 3 ∈ Z_5[x] factors as (3x + 2)(x + 4) and (4x + 1)(2x + 3). Explain why this…

A: UFD- An integral domain in which every non-unit non-zero element can be uniquely  written as the…

Q: Which of the following is a contradiction? ○ ((P VQ) ⇒~ R) ^ (P^Q ^ R) O ((PVQ) ⇒~ R) ^ (Q⇒ (RV P))…

A: Definition:  A compound statement is said to be contradiction if it is false in all cases of…

Q: Use the Binomial Theorem to expand the expression (3x + 2y). Show your work.

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Q: prove R is not homomorphic to R^2

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Q: For what value of k is x+1 a factor of x^4+2x^3-3x^2+kx+1 in ℤ_5[x]?   1 2 3 4 None of the above

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Q: (P^Q)^(P = ¬(Q^R))^(S = R) = -S

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Q: Let p=17. If a belongs to F_{17} and a is non zero , compute the value of a^{16}(mod 17) for a=3 .

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