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: -1 X+1

A: ∫x6-1x2+1dx=∫x6x2+1dx-∫1x2+1dx=x55-x33+x-arctanx-arctanxAdd a constant to the…

Q: Find the coefficient on x^10 in each of the generating functions below. (h) (1-x^14)/(1-x)

A: Find coefficient of x^10

Q: Show that MnXn and Rn^2 are isomorphic.

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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: The opening value of a stock index on the first day of trading from 1994 to 2010 can be modeled…

A: Given The opening value of a stock index on the first day of trading from 1994 to 2010 can be…

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

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Q: Find the inverse, if it exists, for the given matrix. 5-9 4 -7 ... Select the correct choice below…

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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: Consider the function f(x)=x^3−x^2−52x+160. When f(x) is divided by x+8, the remainder is 0. For…

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Q: If f (x) = 3x ^ 4 + 5x ^ 3 + x ^ 2-2 then write f (x) as the product of irreducible terms of Q

A: We have to express f(x) as the product of irreducible terms of Q.

Q: x6 · 6x² + 12x² - 13 = 0. -

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

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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: Write g(x) = x² + x³ + 2x²+x+2 as a product of irreducible polynomials over 2.₂. за

A: Write as a product of irreducible polynomials over .

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

A: Given,      (3+3i)5

Q: 4 -7 -3 -2 8. Let A = [^, and 8 = [ -21. Compute A-1B. -1 2 1

A: first we compute A^-1 by using formula

Q: 4x-3x² +1 (7) x-2

A:

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: Find the remainder when dividing the polynomial x^3-4x^2-7x+2 by x-5

A: detailed solution is given below

Q: Find all the zeros of P . P(x)= x^3 + 3x^2 -4

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Q: Construct a polynomial from the data (1,4),(3,14)(5,19),(7,21),(4,23),(11,21) and also find…

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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: Let f(x) =  x^3 - x^2 -10x - 8 Factor f(x) into linear factors a) (x-1)(x+4)(x-2) b)…

A: Option (c) is correct See the calculation below

Q: 0² d0

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Q: Show that the polynomial p(x) = -x^3+x^2+1 has a root in [1,2]

A: We can check for the values of p(x) :

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: 2log_

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

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Q: What is the fermat value, in polynomial form, of integer 'a', if a=x^4 + 1; p=x^2 + 1?

A: We have to find the Fermat value 'a' which is given in the following form, a=x4+1p=x2+1

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.