Factor 10+ 4i into product of primes Z [i], (Hint: Ille= (2)(2)(29)) in %3D

Given (xi, x2024) Vi = 0,...,n, where x0 = -1, x₁ = 0, x2 = 1, x3 = 2, ..., xn = n = 1. Write down the interpolating polynomial with the least degree when (a) n = 1 (b) n = 2 (c) n = 2024 (d) n = 5000

b) The polynomial, fW) =2x" +mz -3, where m and n are real constants, is divisible by (x+1) but leaves a femiAder remainder of 156 when divided by (X-3). Find the valves of n and m.