Expand f(x)=x2−x +2 as a series of Legendre polynomials

Q: Consider Z[x] = {a,x" + a₁₁x¹+...a₁x+ao: a; € Z,i = 0,1,2,...,n), the set of all polynomials in…

A: Inverse elements are 1 and -1

Q: consider the polynomial equation x3-7x2+14x-4=0 over the interval [0,2].

A: Iteration formula: The iteration formula of secant method is pn+1=pn-1-f(pn-1)pn-pn-1f(pn) -…

Q: Find the remainder when x51 is divided by x + 4 in Z7[x].

A: We have to find the remainder when x51 is divided by x+4 in Z7x. Let t be the remainder when x51 is…

Q: Let p(x) be a polynomial that is divisible by (x-a)n where n∈ N and n >= 2. Prove that p'(x) is…

A: Here, given that the polynomial p(x) is divisible by (x-a)n. So, p(x)=(x-a)nq(x)...(1) Where, q(x)…

Q: Write the polynomial p(x) = x³ - 3x²+x-9 as a Taylor polynomial centered at 20 = 1.

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Q: 1. Express the polynomial f(x) = 4x3 – 5x2 + 2x – 3 as a power of x + 2.

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Q: . Factor x12 -1 as a product of irreducible polynomials over Z.

A: Given: x12-1. We have to factor x12-1 as a product of irreducible polynomials over Z.

Q: For the polynomial below, 1 is a zero. h (x) =x' + 3x- 7x + 3 = X

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Q: Consider the polynomial P (x)=kx' - 5x +3x + 2. Find the value of k such that the remainder is 4…

A: The polynomial is given by Px = kx3-5x2+3x+2 The remainder obtained after dividing the polynomial Px…

Q: product of irreducible polynomials.

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Q: Find the polynomial in x of the third degree, which vanishes when x=-1 and x=2 has  the value 8 when…

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Q: The fourth degree Taylor polynomial for f(z) = 1 centered at a = -3 is T(z) = co +q(x+3) + c(r + 3)2…

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Q: Calculate the first three Legendre coefficients for f (x) = x2 - 1 and then express the f(x) in…

A: Recall the definition of Legendre polynomials.

Q: f (x) = x,³x2² + x1³x3? + x,?x,³ + x,²x3³ + x2³x3² + x2³x3?

A: The given polynomial is not symmetry hence it can not be written in elementary symmetry polynomial

Q: Determine whether the following polynomials are even, odd, or neither. (A) f (x) = 5a – 2a- 4x + 1…

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Q: Find a polynomial that interpolates (−1,0), (0, 2), (1, 1), (2, 2) using the Newton form.

A: x-1012f(x) 0212We have to find a polynomial using the newton form.

Q: For the polynomial below, 1 is a zero. h(x) =x- 7x + 10x- 4 x=(x)4 Express h (x) as a product of…

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Q: Write x3 + 3x² + 3x + 4 in Zs[x] as a product of irreducible polynomials.

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Q: Q// Fit a second-order polynomial to the following data: Y 9 8 3 7 9 11 9 6 1 7 1 3 10 9. 1 a. y =…

A: Given x y 9 8 0 3 7 9 11 9 6 1 0 0 0 7 1 3 8 10 9 1

Q: Find a value for c so that the polynomial y^2+10y+c factors to (y+5)2.

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Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

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Q: Determine whether or not the given polynomial is irreducible over Q (a) x4 - 10x² + 1 (b) (5/2)x+…

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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: Factor x12 - 1 as a product of irreducible polynomials over Z.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Find p(1) and p (-3) of each polynomial. p(x) = x4 - x3 + x - 1

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Q: nsing Eisenstein's criterior of isreducibility show that the polynomiel B p (W) = 3Es lon+0 i's an…

A: The condition for the polynomial to be irreducible is given below

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

A: Given: fx=x3-7x2+8

Q: By using L(x)%3D1and L(x)= 1-x in Lagure polynomials, calculate the value of

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Q: Express f(v) 4 + 6 x² + Z x + 2 in terms of Legendre Polynomials.

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Q: What is Legendre's Polynomial for n =9?

A: The Legendre's polynomialPnx is solution to the Legendre's equation: 1-x2d2ydx2-2xdydx+nn+1y=0 and…