Find a polynomial interpolation to data (-1, 0), (0, 0), (1, 0), (2, 6) using Vandermonde method

Q: What are the advantages and disadvantages of piecewise polynomial interpolation?

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Q: Polynomial P(x)=9x100-5x7-2x2-4 is divided by (x+1). Find the remainder.

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Q: Determine the polynomial function of least degree whose graph passes through the given points.

A: The points (2,6), (3,9) and (5,15) Determine the polynomial function of least degree whose graph…

Q: Explain the other notation which is commonly used for ak in the Newton form of the interpolating…

A: The Newton interpolation polynomial are calculated as: \

Q: Find a linear funtion P(z) = a + a₁ which gives the best least squares fit for the following points:…

A: Given the points -4,0, -2, -2, 4,-9, 5, -8. Now,  x y x2 xy -4 0 16 0 -2 -2 4 4 4 -9 16 -36…

Q: Which of the following polynomials is a difference of​ squares? A.49x^2+64 B.7x^2-8…

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Q: Use the substitution method to evaluate V1-22dx

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Q: ans 1. %3 4x+ 2 9x-3°

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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: Find a polynomial P(z) = a + a₂z+ª₂x² of degree 2 which gives the best least squares fit for the…

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Q: (V10 + V5)(V10 – V5) = (_) – (P = –

A: Given, To solve

Q: Express as a polynomial.

A: Express as a polynomial.         9p4q3-6p2q4+5p3q23p2q2

Q: Find the remainder when dividing the polynomial x^3-4x^2-7x+2 by x-5

A: detailed solution is given below

Q: Then y'(0) 1- 1 2

A: Here we use Newton's Forward Difference Method :

Q: x ^ 4 - 3x ^ 3 + 5x - 6) * (x + 2) ^ - 1 divide polynomials using synthetic division

A: We have to divide polynomials using synthetic division.

Q: Find iterpolation polynomial p2(x) = ax² + bx + c that passess through the points: (0,7), (1,12),…

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Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.