Please comment if you need any clarification.
If you find my answer useful please put thumbs up. Thank you.
Let (r) 2 +ar+ ... +,r" be a polynomial of degree less than or equal to...
Let f(x) = do +212 + ... + and" be a polynomial of degree less than or equal to n, and let {x0, 21, ..., Un} be distinct points. What is the value of f (x0, X1, ... , Xn]? Explain.
let fx be a polynomial of degree <= to n whats the value of f(Xo, X1....Xn). explain Let f(x) = ao tai xt...... + Anxh be a polynomial of | degree less than or equal to n, and let {xo.xi... n} be distinct points What is the value of f[xo, X.. Xn] Justify / Explain.
19. Use Newton's divided difference formula to find the polynomial of degree less than or equal to four, that cos 2, at the interpolation points 0. π/2. π. 3π/2. 2π. Do not approximate π by a number interpolates f(x) with finite digits.
Problem 10.13. Recal that a polynomial p over R is an expression of the form p(x) an"+an--+..+ar +ao where each aj E R and n E N. The largest integer j such that a/ 0 is the degree of p. We define the degree of the constant polynomial p0 to be -. (A polynomial over R defines a function p : R R.) (a) Define a relation on the set of polynomials by p if and only if p(0) (0)...
Question 4 (20 points) Let F: R R be any homogeneous polynomial function (with degree no less than one) with at least one positive value. Prove that the function f:Rn R, f(x) F(x) 1, defines on f-1(0) a structure of smooth manifold.
R(Xwhere the degree of R(x) is less than the degree of D(x) D(x) Use polynomial division to rewrite each expression in the form Q(x) X 8 (a) X 12 16x 9 (b) _ 2x 1 12x2 (c) x2 12 4x 1
Let f(x) = a_0 + a_1x + \cdots + a_nx^nf(x)=a 0 +a 1 x+⋯+a n x n be a polynomial of degree less than or equal to nn, and let \{x_0,x_1,\ldots,x_n\}{x 0 ,x 1 ,…,x n } be distinct points. What is the value of f[x_0,x_1,\ldots,x_n]f[x 0 ,x 1 ,…,x n ]? Explain.
Let f (x) be a monic polynomial of degree n with distinct zeros ai,..., an. Prove -1 Let f (x) be a monic polynomial of degree n with distinct zeros ai,..., an. Prove -1
(i) Show that R is a subring of the polynomial ring Rx. | R{]4 (ii) Let k be a fixed positive integer and be the set of all polynomials of degree less than or equal to k. Is R[xk a subring of R[a]? 2r4+3x - 5 when it is (iii) Find the quotient q(x divided by P2(x) of the polynomial P1( and remainder r(x) - 2c + 1 in - (iv) List all the polynomials of degree 3 in Z...
(i) Show that R is a subring of the polynomial ring Rx. | R{]4 (ii) Let k be a fixed positive integer and be the set of all polynomials of degree less than or equal to k. Is R[xk a subring of R[a]? 2r4+3x - 5 when it is (iii) Find the quotient q(x divided by P2(x) of the polynomial P1( and remainder r(x) - 2c + 1 in - (iv) List all the polynomials of degree 3 in Z...