Question

When x^4 + ax^3 + bx +c is divided by (x–1), (x+1), and (x+2), the remainders are 14, 0, and –16 respectively. Find the values of a, b, and c.

Answer 1

do a little synthetic division. The remainder when divided by (x-1) is a+b+c+1. So, one equation is

a+b+c+1 = 14

do the others, then solve the three equations for a,b,c.

Answer 2

first division -> a+b+c-1 = 14
second division -> c-a-b+1 = 0
third division-> have to go, continue ;)