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

Q: 2. Use syntr dhe hirst polynomial by the second. а. х2+x -3; х-1 b. 4x- 3x2+ 3x - 2; x-1 c. x'+x°…

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Q: 29. Write a third-degree polynomial f(x) with integer coefficients and zeros of i, -3, and 3.

A: Given  zeros of a third degree polynomial 14,−12 and 3

Q: The polynomial p(x) = 2-(x+1)+x(x+1)- 2x(x+1)(x–1) interpolates the first four points in the table:…

A: Given, the polynomial p(x)=2-(x+1)+x(x+1)-2x(x+1)(x-1)   interpolates the first four points in the…

Q: Which of the following Polynomial satisfies the condition that all of its roots is a root of…

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Q: Express the polynomial a+ 3 +a2 + 2r as a product of its irreducible factors in Z,lr).

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Q: Show that the polynomial 2x + 1 in Z4[x] has a multiplicative inversein Z4[x].

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Q: 4. Write a polynomial to express the total value, T(x), of (x + 4) 20-Peso bills (x – 3) 50-Peso…

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Q: Find the decomposition and give the proper order of the composition 3x2 given F(x) = -(2x - 7)7 +. 2

A: F(x)=-(2x-7)7+3x22

Q: Fit a second-order polynomial to the data in the kollowing daha- 0|12/31415 yi 2.17.713.6|272 40.9…

A: The objective is to find a second order polynomial and to find the standard error.

Q: The number of zeros of the polynomial x+4x +1 in Z, is. O None O 2 O 4

A: solution of the given problem is below

Q: Use the Remainder Theorem to find the remainder when e ded by the corresponding binomial. 1. x3+2x2+…

A: using remainder theorem to find the remainder when the polynomial divided by corresponding binomial1…

Q: 5. For how many different integers bis the polynomial x² + bx + 16 factorable over the integers?

A: From the given data

Q: The number of zeros of the polynomial x² + 3x +2 in Z, is: O 1 O None O 2

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Q: Find the recursion formula and a fourth degree polynomial approximadion for the power serîies…

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Q: ] 5. Consider h(x) = (x³ + 2)². (a) Expand h and compute h' using the power rule and polynomial…

A: Explanation of the answer is as follows

Q: Write the closed form of the summation as a polynomial in n. 1. 3i + 3

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Q: How do i find the ral seros of  a given polynomial and their corresponding multiplicities?…

A: We have to find the zeroes and their multiplicities.

Q: Find a fourth-degree polynomial with integer coefficients that has zeros 5i and –1, with -1 a zero…

A: Given: A fourth degree polynomial has zeros 5i and -1 , with -1 a zero of multiplicity 2.

Q: Find the coefficient of at in the product (1 + 2a)* (2 – a) using binomial

A: Introduction :

Q: Q3: Factorize f (x) = 2x* + x³ + 2x + 4 € Z5[x] as a polynomials product to irreducible over Z5?

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Q: 1. It is known that the polynomial p(x) = 2 – (x + 1) + x(x + 1) – 2æ(x + 1)(x – 1) interpolates the…

A: Solution by using Newton's forward difference interpolation method .

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: (b) Find the nested form Q(x) of the polynomial /(x) = x³ + 2x2-5x + 3 and hence evaluate Q(2.6)…

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Q: Find the Taylor polynomial 7₂ for the function 3 O3+ (x-1)+(x-1)² 54 f(x)=√8+

A: We have to find the Taylor polynomial for the function f(x) at the number a=1. And power series…

Q: Let f (x) = x4 − 7x3 + 6x2 − 4x + 1. The coefficient of x8 in the 8th Taylor polynomial p8 is

A: Application of derivative

Q: Find the residue f(z) = Z²-22 (2+1)² (2²44)

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Q: D. Find a fourth-degree polynomial with integer coefficients that has zeros 3i and -1, with -1 a…

A: The given zeros are 3i,-3i,-1 and -1.

Q: Express p (x) = x3 as a Taylor polynomial about a = 1/2

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Q: Find the zero(s) of the polynomial ³ - x²-3x+3.

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Q: 1. Find the sum of the polynomials: (5x°-2x+x)+(4x° – 3xª +2x³-5x) O x5 +3x4-4x3+6x O 9x5+3x4-4x³+6x…

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Q: I. Use the Factor Theorem to determine whether the given binomial of the form x - cis a factor of…

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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: Prove using the generating function of the Legendre Polynomials: t2 [xP(x) – nP,(x)]t": (1- 2xt +…

A: We have to prove ∑n=0∞xPn'(x)-nPn(x)tn=t21-2xt+t232 We know the generating function of the Legendre…

Q: Which of the following polynomials in Z3 [x] is irreducible? (a) p (x) = x ^ 3 + x + 1 (b) p (x) =…

A: Useful result: If f(x)∈F[x] be a polynomial over a field F of degree two or three. Then f(x) is…

Q: I. Use the Factor Theorem to determine whether the given binomial of the form x - c is a factor of…

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Q: The standard notation of the factorial polynomial x(4) - x(3) - 2

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Q: Find the conditions that the zeroes of the polynomials Ax) =x – px+ qx – r may be in arthametic…

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Q: a) Factor a +x³ + x into irreducible polynomials in Z2[r];

A: i) Linear factors are irreducible. ii) Just substitute values in Zp and see the expression becomes…

Q: Find the Taylor polynomials p3 and p4 centered at a = 0 for ƒ(x) = (1 + x)-3.

A: Given that: The function f (x) = ( 1+x) - 3 .

Q: Consider the polynomial f(x) = 25x - 9x* + 3x? - 12 %3D show that it is irreducible in Q[x]

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Q: Express the second order polynomial p(x) = x^2 + 4x + 13 in the sum of square form

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Q: 1. Use the Factor Theorem to determine whether the given binomial of the form x - cis a factor of…

A: Given:- f(x) =4x3+4x2-11x+4  To find:- Use the Factor Theorem to determine 2x-1 is a factor of the…

Q: Find the LCM of the given polynomial. x3 - x,    x2 - x

A: To find the LCM of given polynomial: x3-x,x2-x. Solution: x3-x=x(x2-1)⇒x3-x=x(x+1)(x-1)…

Q: x5 + (2i – 1)x³3 – 2ix – 5 a = 1- i

A: given that…

Q: Which of the following polynomials has zeros at x = -6 (which is a bounce point), and x = 4 (which…

A: Given data  Polynomial has zeros at x=-6(bounce point) Polynomial has zeros at x=4(cross point)…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 3 and…

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Q: ind the critical points, A and B, of the following polynomial (with A < B). f(x) = 6x³ + 18x² – 630x…

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Q: Find the critical points, A and B, of the following polynomial (with A&lt;B). f(x)=2x^3−24x^2+5 A=B=

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Q: Find the fifth Taylor polynomial of x3 - 7x2 + 8 at x = 0.

A: Given: fx=x3-7x2+8