polynomials

Q: The polynomial that passes through the following x-y data (18, y,), (22,25), (24,123) is given by…

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Q: Show that the Newton divided-difference polynomials 3 - 2(х + 1) + 0(х + 1)x + (х+ 1)x(х — 1) аnd…

A: Given,

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: a) Calculate f(3.4) using Newton's interpolating polynomials of order 1, 2 and 3. All numeric values…

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Q: Determine the interpolating polynomial in Newton's form that passes through the points and Use the…

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Q: Prove that x4+4=(x+1+i)(x+1-i)(x-1-i)

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Q: Consider the data (1, 10), (3,6). Then, Newton's polynomial that interpolates the data is

A: Given point is, Then,

Q: A polynomial f (x) with real coefficients and leading coefficient 1 has the given zero(s) and…

A: Given- Consider the roots 3+5i and -1-i. To find- A polynomial f (x) with real coefficients and…

Q: QUESTION 11 Express the polynomial x3+2x+3 EZ-[x]as a product of irreducible polynomials of Zs[x]:…

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Q: Consider the data (1,10), (3,6)(1,10), (3,6). Then, Newton's polynomial that interpolates the data…

A: Solution of given problem is followed by Newton's interpolation formula.

Q: From the given data, identify f(4) using Newton's polynomial. (2,10), (3,15), (5,25), (8,40)

A: Explanation of the solution is given below....

Q: a) Show that the cubic polynomials P(x) = 3 − 2(x + 1) + 0(x + 1)(x) + (x + 1)(x)(x − 1) and Q(x) =…

A: Given two cubic polynomial,

Q: mial x3+2x+3 EZŞ[x] product of irreducible polynomials of 75[x]- e se

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Q: Show that the Newton divided-difference polynomials 3 — 2(х + 1) + 0(х + 1)х + (x + 1)x(х — 1) and…

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Q: Use Lagrange interpolating polynomials of order 4 to calculate (7.1) 1 3 8 Ax) 1 20 94 267

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Q: Show that the Newton divided-difference polynomials 3 - 2(х + 1) +0(х + 1)х + (х + 1)x(х — 1) and…

A: A polynomial P(x) is called an interpolating polynomial if the values and / or its certain order…

Q: 4. Prove Theorem 2.6.5.

A: Let p,q be any two distinct points on l. Let r be any point on l. Let m be the line containing p and…

Q: Find the first 3 Maclaurin polynomials?

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Q: .5) a) Express the polynomial f(x) in terms of Legendre polynomials where f(x) = 1-3x + 3x2

A: Given ,            f(x) = 1-3x+3x²

Q: (a) Develop a table of f(x)=2e* + 3x for x = 3, 5, 7 and 9. (b) Estimate f(4.2) using the…

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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: A polynomial f (x) with real coefficients and leading coefficient 1 has the given zero(s) and…

A: To express f(x) as a product of linear and quadratic polynomials with real coefficients that…

Q: Determine the 3rd degree polynomial for the given set of data(x.y). 1. 1.3 2.4 3.7 3.8 5.1 y -6.3…

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Q: Multiply the polynomials (x-1)(x* +x³ + down an identity for (x - 1)(x" +x"-1 +..+x² +x + 1) for n a…

A: Multiply the given polynomials using table (x-1)(x4+x3+x2+x+1)   x4 x3 x2 x 1 x x5 x4 x3 x2 x…

Q: 5. а) Factor the polynomial f (x) = 3x*+2a³ +2x² +2x– 1 into irreducible polynomials %3D in C[r],…

A: "Since you have asked multiple questions, we will solve the first question  for you. If you want any…

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

A: The solution of the differential equations are the functions that satisfies the differential…

Q: what is the approximate value at point x- 0.7 of the interpolation polynomial obtained using the…

A: We have the following values: x y -1 4 0 11 1 16 2 13 Now, let make the backward…

Q: Determine the 4th degree polynomial for the given set of data(x.y). 1. 1.3 2.4 3.7 3.8 5.1 y -6.3…

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Q: Test the sets of polynomials for linear inde­pendence. For those that are linearly dependent,…

A: We have to determine whether or not we can find real numbers r, s,t, which are not all zero, Such…

Q: (a) Show that (x2 + v2x + 1)(x² – v2x + 1) = x* + 1.

A: Given that: (x2+2x+1)(x2-2x+1)   NOTE: As per our answering guidelines, we can only answer 1…

Q: Calculate the 1st order Newton polynomial that interpolates the two data points (1,1),(2,3). Now…

A: We can use Newton's forward difference interpolation method to find Newton's polynomial.

Q: ind second order polynomial that interpolate all the data in the able using Newton's DD method -5 1…

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Q: snip

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

Q: Show that the Newton divided-difference polynomials 3 – 2(x + 1) + 0(x + 1)x + (x + 1)x(x – 1) and…

A: Given: Let P(x)=3-2x+1+0x+1x+x+1xx-1    Q(x)=-1+4x+2-3x+2x+1+x+2x+1x

Q: A car traveling along a straight road is clocked at a number of points. The data from the…

A: Initially  Use a Hermite polynomial to predict the position of the car and its speed when t = 10 s.…

Q: Factor f(x)= 4x^3+27x^2-39x+8 into linear factors given that -8 is a zero of f(x).…

A: Given: f(x) = 4x3+ 27x2 -39x+8 and -8 is a zero of f(x)  To find: factor f(x) into linear factors

Q: Example Let f(x) = sin(x). Approximate f() by the Hermite interpo- lating polynomial of degree at…

A: Given the function fx=sinπx To find the value of f14 by Hermite interpolating polynomial when x0=0,…

Q: Calculate f (3.4) using Newton.s interpolating polynomials of order 1 through 3 and estimate the…

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Q: Show that I (x) = 2x - 18 is invertible. What are the domain and range of 1- 1?

A: Ix=2x-18 Now let, y=2x-18 Now to find inverse function interchange x and y, then solve for y in…

Q: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zero and degree.…

A: Given :- zero :- 5+9i and degree =2 To find:- A polynomial f(x) with real coefficients and leading…

Q: Let f(x) = x3+5x+3. Construct the divided-difference table based = 2, a2 3, a3 - 4, x4 5, axs 6, and…

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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: -2 21 -9-21 1- FIND THE INTER POLATION POLYNOMIAL BY USING THE FOR THE ABOVE NEWTON DIVIDED…

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Q: A scientist has executed one experiment to identify the values of an unknown function f(x). The…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: #37

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Q: which are polynomial functions f(x)=4^x  -1 g(x)=7x^4  -10x^2  -9 h(x)=tanx

A: Hi, Thank you for the question. Since you have posted a question with multiple sub parts, as per the…

Q: A polynomial f (x) with real coefficients and leading coefficient 1 has the given zero(s) and…

A: Given Zeroes= 4+3i, -2+i therefore conjugate of above zeroes are also zeroes of f(x) Therefore 4-3i,…

Q: (a) Table 1 shows the COVID-19 data in Malaysia. Compute using Lagrange Interpolating Polynomial: i.…

A: The covid-19 data in Malaysia x 3 4 5 6 c(x) 2 5 7 3 The Lagrange interpolating polynomial…