Factorize (i) 1144 in Z (i) 1144 in Z[i] (ii) 1144 in Zp[x] where p is a Z-prime greater than 1144.

Q: 2 17. The polynomial P(x) = x* - &x – of x = 1, 3, and -2+i. What is its fourth zero? 8x +15 has…

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Q: What is the coefficient of xy³ when (2y-x)° is expanded by the binomial theorem?

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Q: The coefficient of x²y4z5 in the expansion of (3x+y+z)¹¹ is

A: The given expression is: (3x + y + z)11 To find: The coefficient of x2y4z5 in the expansion of (3x +…

Q: Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

A: We have to check whether the polynomial x4-2x3+6x-3 is irreducible over the set of rational numbers…

Q: Determine which of the polynomials below are irreducible over Q. (a) a" + 9xª + 12:r² + 6 (b) a* + x…

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Q: Find the first 3 Maclaurin polynomials?

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Q: Which polynomial has the zeros 1, –1, & -4? O y = (x+1)(x – 1)(x+ 4) O y = (x+1)x –1)(x – 4) o y…

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Q: If the sum of the coefficients of all even powers of x in the product (1 + x + x² + ... + x2n) (1 –…

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Q: 4. (a) Compute the cyclotomic polynomial P14(x). (b) Express x6 factors. 1 as a product of…

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Q: Find the coefficient of x5 in (1 – 2x)-7 using generating function.

A: Given to find the coefficient of x5 in 1-2x-7 The generating function will be Gx=1-2x-7…

Q: Show that each 952 MXT (a) x² + 2x³ + x + 1 polynomial is irreducible in Q[x], (b) x42x² + 8x +…

A: Please post b part complete it's not visible

Q: Expand the f(x) = 10 + 8x +9x² in a seried of Legendre polynomials. O a 13P,x)– 8P,(x) – 6 P, (x) O…

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Q: Determine Q(x) when P(x)=x³-5x2-3x+2 is divided by x-1 and then expressed in the form Select one: O…

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Q: Compute the constant term in the expansion of (2x³ + ½)¹².

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Q: 2. Divide the following polynomials using long division, and indicate the quotient Q(z) and the…

A: We have to find

Q: In the characteristic polynomial (3 – A)(4 – A)³(–3- )(3 – 1), what is the multiplicity of d = -3?

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Q: (c) How many of the elements of Z186 have multiplicative inverses?

A: To find the number of elements in the set of integers modulo 186, which have multiplicative inverse.

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Find the coefficient of x7 in (1 + x + x² + x³ + x4 + ...)¹3

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Q: (d) Show that x² + x +4 is irreducible over Z11. (e) Write x³ + x² + x +1 as a product of irrducible…

A: An irreducible polynomial is a non-constant polynomial over a field that cannot be factored into the…

Q: 3. Consider the polynomial p(z) = 2³ +2²+z+1. (a) Verify that i is a root of p. (b) [ACS] Find the…

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Q: Given (xi , xi2022 i ) ∀i = 0, ..., n, where x0 = −1, x1 = 0, x2 = 1, x3 = 2, ..., xn = n − 1. Write…

A: Given xi,xi2022∀i=0,1,2,...,n  Where x0=-1, x1=0, x2=1, x3=2,..., xn=n-1

Q: Find the standard inner product on P of the given polynomials. p= -2+ 4x + a2, q = 3+ 4x 3a2. (p, q)

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Q: Express the polynomial in the form an(x - ₁)(x-₂)(x-rn). x² + 11

A: The polynomial is given by x2+11 To determine: The expression of the polynomial in factored form.

Q: Which of these polynomials has a zero of multiplicity 3 at z = 1? a. p(r) = xª + 5x³ + 5x² – 5x – 6…

A: If x=a is a zero with multiplicity n of a polynomial, then x-an is a factor of the polynomial. a.…

Q: Let q(n) be the sum of the squares of the first n odd numbers. For example: q(0)  =  0 q(1)  =…

A: If n is any odd integer greater than 0 (i.,e., odd positive integer) then it's general form is 2n-1…

Q: What is the least coefficient in the expansion of (x -1)7?

A: Use Pascal's Triangles to find least coefficient in the expansion of (x -1)7