Find the coefficient of X^35 in the generating function (x^4+x^5+x^6+x^7+x^8)^5 (Show work and leave final answer in C(n,r) form.)

Q: (a^2 + 1)(b^2 - 1)=c^2 + 3333 prove that it doesn't have an integer solution

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Q: Show that x = 1 is the only zero of the polynomial x^25 − 1 over Z_37

A: The elements of the sets Z37 are {0,1,2,3,.......,36}

Q: Which of [0], [1], [2], [3], [4] is equal to [3]^2023 in Z_5? What is [15]^1989 congruent to in…

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Q: x + 2x + 34 (* – 10)(x^ – 25)²(,² – 8) -

A: Step:-1 Partial Fractional:- The Partial fractional is a process of taking a rational expression and…

Q: (x ^ 4 - 3x ^ 3 + 5x - 6) * (x + 2) ^ - 1 divide polynomials using synthetic division

A: We have to divide the polynomial using synthetic division…

Q: Use the given real ZERO of the polynomial function to find the remaining real ZEROS. f (x)= 380x² +…

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Q: Suppose that p(x) = x^3+ ax^2 + x + 1 has a zero at x = 1, where a is some constant. Determine a,…

A: given p(x)=x3+ax2+x+1 has zero at x=1 Therefore substitute x=1 and equate with 0…

Q: Differentiate y O 1 4x +2 = x(x-1) (2x²(x + 1)) 3(x-1)²(x²+2x+1) 8x² + x 2 2 O3(x-1)² (3x²-1) 8(x² +…

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

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

A: We have to solve given problem:

Q: Find the gcd of (x^4+x^3+x^2+2x+3) and (x^3+4x^2+2x+3) in Z5.

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

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Q: Factor the polynomial equation n ^ 4 - 49n ^ 2 = 0

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Q: form of (3+3i)^5

A: Given,      (3+3i)5

Q: Find the coefficient of x11 in (x2 - 3x) / (1 - x )4

A: Solution:

Q: Express x8 - x as a product of irreducibles over Z2.

A: The given polynomial x8-x. We have to write the polynomial as a product of irreducibles over ℤ2.

Q: 4x-3x² +1 (7) x-2

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Q: I am trying to find out if the polynomial 12x^4+8x^3+9x^2+4x+4 is reducible or irreducible over Q.…

A: The given polynomial is, 12x4+8x3+9x2+4x+4

Q: Show that 1 + i is a root of x* - x' + x2 + 2. Use this fact to decompose the polynomial into a…

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Q: When dividing x^3+2x+4 by 3x+2 in Z7[x], the remainder is * O 4 O None of the choices 2.

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Q: Prove that m^3 + 2n^2 =36 has no solution in positive integers.

A: Prove that  there is no solution for positive integers.Let if for for

Q: (2x - 7x - 1) - (-2x + 3x- 4) Subtract 5x + 2x -1 from 4x +3

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Q: x ^ 4 - 3x ^ 3 + 5x - 6) * (x + 2) ^ - 1 divide polynomials using synthetic division

A: We have to divide polynomials using synthetic division.

Q: The product of 2x3 + 3x2 +1 and 2x2 + 4 in z5 [x]/ is: X^2+2 None 5x^2+ 5x +1 O 4x+1

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Q: OUp3 Fee/X = 0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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: Find a polynomial p(x) = ao + a1x + aza² + azx³ of degree < 3 (here ao, a1, a2, a3 are real numbers)…

A: In this question , use the given values and solve the equations and find the polynomial.

Q: The number of zeros of the polynomial x^2 +4x+1 in Z6 is:

A: See the detailed solution below.

Q: What is the factored form of x2+11x+14

A: Given : 2x2 + 11x + 14

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: Find the general antiderivative. f(3 sin x-3cos.x) dx Select One 3cosx + 3sinx + c -3cosx - 3sinx +…

A: We have to find antiderivative.We have to find solution.

Q: Express x8 - x as a product of irreducibles over Z2.

A: Given polynomial is fx=x8-x. To Express: The given polynomial fx=x8-x as a product of irreducible…

Q: 35. How many times is 2 a root of x6 - 9x4 + 24x² - 16 = 0?

A: Given equation x6-9x4+24x2-16=0

Q: 1. x + 11x + 10 2. x - 12x + 27 3. x - 4x + 5 4. x + x - 20 6. x - 7x - 44 +6x : Not Factorable : (x…

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Q: (b) In Z/12Z,      ((15) ̅- (4) ̅ ) · ((8) ̅+ 7 ̅)^2 · ((3) ̅+ (11) ̅ )     = (11)– . (3)–^2 .…

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