a) Use Newton interpolation to find the unique cubic polynomial f that passes through the points (0, 1), (1, 1), (2, 1), (3, 4). If we write f as a linear combination of binomial polynomials f(x) = E a. (), what is the coefficient a2 ? %3D O 1 O -2 -3 2)

Q: A polynomial expression is given. 3z (zy) 21'y Which is an equivalent form of the expression? 3y 3y

A: Explanation of the answer is as follows

Q: 2. Given the points (1,0.7),(2,0.73),(3,0.8),(4,0.75),(5,0.6). Use Lagrange polynomials to find the…

A: Given points are xi 1 2 3 4 5 yi 0.7 0.73 0.8 0.75 0.6 Here, i=0, 1, 2, 3, 4.

Q: Also, our definition of the first 4 Legendre polynomials is: 1 Po(x) V2 P1 (x) = V5/2 (1 – 312)…

A:

Q: 1) Factor f(x) = 2x3 + (-3-2i)x? + (-3- i)x + (2 + i) into linear factors 2 +i is a zero of the…

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

Q: Use nested multiplication algorithm to convert the polynomial 1+2x+3x² into its equivale Newton form…

A: In this question, the nested algorithm to convert the polynomial 1+2x+3x2 into its equivalent Newton…

Q: Factor completely. qs - 8s + qf - 8f qs - 8s + qf - 8f =

A: We have to complete factor

Q: Let P(x) be the interpolating polynomial for the data (0, 1), (1,3), (4, -3). Then P(2) = 3 4 -3 1

A: Here are 2 ways to solve find the solution In 2 method we will use this lagrange interpolation…

Q: Find the Lagrange interpolating polynomial for this table 2 2.5 34 -1/3 3/32 4/3 25 I Y

A:

Q: Find a fourth degree polynomial that has zeros of 1, -3, 2i.

A:

Q: Use Cramer's rule to find only the value of x2 , where a is a positive real number. 2x2 – x3 + x4 =…

A:

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…