Show that the polynomial interpolating the following data has degree 3. 비 f(x) 1 4 11 16 13 X -2 0 1 2 3

Q: Write a possible function for the polynomial shown: 3- 2- 1+ -2 -1 -1+ -5 -4 4 6. 72 3- 4-

A: Since given polynomial has zeros as x=-3,2,2,5 Therefore, possible function can be

Q: Describe the end behavior of the polynomial described: 1.)y = ax3, α>0 2.) y = ax*, a 0 %3D 4.) у…

A: Consider the first equation: y=ax3, a>0 Degree of equation is 3 which is odd. Leading…

Q: (x) = 5x5 + ax4 bx³ + cx – 3 O As*→00, y0o. As→-∞, yH0 O As*→00, y0, Ast→-0, y→-00 O As*→00, y→-00,…

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Q: What are the zeros of the polynomial function x² + 5x+6 Ox= -2,-6 Ox= 3,5 O x = -2, -3 x= -1,6…

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Q: It is desired to have the first joint of a six-axis robot go from initial angle of 100 to a final…

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Q: e down a polynomial of degree exactly 4 that interpolates the four points: (-1,-5 1), (2, 1), (3,…

A: We have to find the polynomial equation from given points.

Q: 2. Find the polynomial the passes through the following points (0,0), (2, —2), (4,0)

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Q: Determine the third order polynomial below which has the following cartesian coordinades (-1,-16),…

A: Let the third order polynomial is  ft=at3+bt2+ct+d The points -1,-16,0,-7,2,-13 and 5,8 are on y=ft…

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: A third degree polynomial passes through the points (0,9), (1.14), (2,17), (3,24), (4,41), (5,74)…

A: The value of X1=∆y3=y4-y3=24-17⇒X1=7and value of ∆2y2=X2=∆y3-∆y2=7-3=4⇒X2=4

Q: A constant temperature, pressure-volume thermodynamic process has the following data: Pressure 420…

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Q: What is a polynomial in x?

A: The x happening in a polynomial is generally referred to as a variable or an indeterminate. When the…

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: define polynomial .

A: Consider the given information as define polynomial

Q: 2. Verify that polynomials interpolate the data p(x) = 5x³ 27x² + 45x - 21 q(x) = x¹ - 5x³+8x² −…

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Q: 2. Write a computer code that interpolates the function f(x) = 1+2 at the points -5, -4, -3, -2, -1,…

A: Here is the code:import numpy as np import matplotlib.pyplot as plt # Define the function def f(x):…

Q: Define the Newton form of the interpolating polynomial?

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Q: What is the polynomial of degree zero

A: Degree of Polynomial: In a polynomial highest power of variable is called degree of polynomial.

Q: For which function defined by a polynomial are the zeros of the polynomial-4 and-6? 1) y=x² -10x-24…

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Q: Check whether or not x³ + 2x + 1 € F5[x] is a primitive polynomial.

A: Primitive polynomial

Q: what could be a polynomial with a degree of 5 if its zeros are -2,1, and 4?

A: The given zeros are, –2, 1 and 4.

Q: It is possible to write xk as a linear combination of Chebyshev's polynomials, for example %3D…

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Q: Discuss the properties of 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