Write x3 + 2x + 1 as a product of linear polynomials over someextension field of Z3.

Q: What are Bernstein polynomials?

A: A polynomial is basically a function, which can either be quadratic, cubic and so on in which the…

Q: Find Tay br Polynomial. for the function fox): Vx + 3. ot degree 3 centered ata=2

A: According to the problem, we have

Q: y = exp( 2-x ) at x = [-1,2].

A: Given   y=e(2-x) , in the interval x=-1,2 So the value of y at x=-1,0,1,2 are…

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

A:

Q: Suppose ƒ(0) = 1, ƒ'(0) = 2, and ƒ"(0) = -1. Find the quadraticapproximating polynomial for ƒ…

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Q: Are there any nonconstant polynomials in Z[x] that have multiplicativeinverses? Explain your answer

A: No, there is no any nonconstant polynomial in Z[x] that have multiplicative inverse.

Q: Find the monic quadratic polynomial, q(x), such that •1

A: Given:

Q: Which type of polynomial satisfies f 111(x) = 0 for all x?

A: To find: The polynomials that satisfy f'''(x)=0

Q: Let p, = 2t – 1 and p2 = t3 +2. Write three polynomials that are in span{p1, P2}-

A:

Q: 2. Is the following set of polynomials linearly independent in P2? Explain your work. (-1+2t + 3t?),…

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Q: Express f (x) = x + 3x - x2 + 5x – 2 in terms of Legendre polynomials.

A:

Q: ld and p (x) be an irreducible polynomial of positive degree over a

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Q: What is a polynomialfunction in degree 1

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Q: A simplified polynomial that has exactly one term is called a/an ............ ?

A:

Q: Formulate that the Lagrange interpolation polynomial that passes through points (0, 3), (1,4) and…

A: To show that the Lagrange interpolation polynomial that passes through points (0,-3),(1,4),(2,15) is…

Q: Ex.5 - Prove that the polynomial 2ª + z + 1 has exactly two zeros in the right half-plane.

A: Solution: We will be using the method of Routh array For a polynomial Qz=anzn+an-1zn-1+...+a1s+a0…

Q: A simplified polynomial that has two terms is called a/an ............ ?

A:

Q: Find ALL irreducible polynomials of degree 2 or 3 in Zr].

A: An irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the…

Q: In Z4{x}, find two distinct polynomials that determine the same function for Z4 to Z4.

A: we have to find two polynomial Z4 {n} which determine the same function for Z4 to Z4. Let us…

Q: product of irreducible polynomials.

A:

Q: Let the chor a cteristic polynomial A, detlA)=? Then

A: Given that: Characteristic Polynomial of A:          ∆A = λ(λ2+1)(λ+1)

Q: Explain the formula for the Hermite interpolating polynomial?

A: In any polynomial function if the values for the function is known for some data points and the…

Q: If a polynomial cannot be written as the product of two other polynomials (excluding 1 and - 1),…

A: We know that a prime number have only 1 and that number as its factors.

Q: Expand: Write as a polynomial. (2x - 3y)

A: Given,2x-3y4=2x-3y22Using,a-b2=a2+b2-2abtherefore,=2x2+3y2-22x3y2=4x2+9y2-12xy2Now,using,a+b+c2=a2+b…

Q: EXERCISE 5.4 Factorize each of the following cubic polynomials by factor theorem. 2 x --22x + 40 5.…

A: 8. Cubic Polynomial: 2x3+x2-2x-1 Take x2 common from the first two terms of the given polynomials.…

Q: Use the Intermediate Value Theorem to show that thefunction f1x2 = 4x3 - 2x2 - 7 has a real zero in…

A: Given: fx=4x3-2x2-7; x∈1,2 We know that for a polynomial functiony=fx in x∈a,b, if fa and fb have…

Q: Determine the linear Lagrange interpolating polynomial that passes through the points (2, 4) and (5,…

A:

Q: Determine the third degree Newton polynomial which passes through the data points (0,1); (1, 0); (2,…

A: The objective is to determine the third degree Newton polynomial which passes through the data…

Q: Sketch a higher degree polynomial with the following roots: -2, 3, -3, 6. f(x) 9,

A: It is given that the roots are -2, 3, -3 and 6. That is, x+2=0, x-3=0, x+3=0 and x-6=0. The…

Q: List all the polynomials of degree 2 in Z2[x]. Which of these areequal as functions from Z2 to Z2?

A:

Q: 1. Determine whether the set S = {2x² – 14x + 34, 3x – 4, x² + 5x + 1} is linearly independent or…

A: Here first we check the set s is linearly dependent or not.

Q: Define the Newton form of the interpolating polynomial?

A:

Q: Show that the polynomial z5 + 14z + 2 has four zeros in the annulus </2 < 2.

A: Given

Q: A farmer’s rectangular field has an area that can be expressed as thetrinomial x2 + 2x + 1. In terms…

A:

Q: Write a polynomial function of least degree with integral coefficients that has the given zeros. + 0…

A: topic- polynomials

Q: Express p(x)= x3 as a Taylor polynomial about a = -1.

A: The Taylor polynomial of degree n about  is given by:f(x) = f(a) + f'(a)(x-a) + f''(a)2!(x-a)2…

Q: Are u able to do polynomial fitting without any mathematical tool? Why?

A: Polynomial fitting manually: a: Polynomial coefficient k: degree of polynomial N: no. of points to…

Q: snip

A: Given{x,2x-x2,3x+2x2}To check dependentIf they are dependent , need to express  one function in…

Q: Write the polynomial f(x) that meets the given conditions. Degree 3 polynomial with interger…

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

A:

Q: Plot the zeros of each polynomial on a line together with the zeros of its first derivative. i) y =…

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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: Show that f (x) = 7x − 4 is invertible and find its inverse.

A: To show that the given function f(x) is invertible and find its inverse.

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

A:

Q: Express f(x) = 4x3 + 6x2 + 7x + 2 in term of Legendre Polynomials.

A: The Legendre equation is, 1-x2d2ydx2-2x dydx+nn+1y=0 The polynomial denoted by Pnx is called the…

Q: Find the polynomials whose zeroes are (i)3,-4 and (ii)3, 3.

A: First I have written a short note about , how to a polynomial us given, when two of its zeros are…

Q: 2a] aS a product Of irreducible polynomials.

A:

Q: xỉ + x + x – X1X2X3

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.