Question

By remainder theorem, find the remainder of p(x) when it is divided by g(x), where p(x)= x^3-2x^2-4x-1, g(x)= x+1

Answer 1

By the remainder theorem the remainder when dividing p(x) by x-a is p(a).

Dividing by x+1 means we want p(-1).

p(-1) = (-1)³ - 2(-1)² -4(-1) - 1 = -1 - 2 + 4 - 1 = 0

Answer: 0

They go in evenly so x+1 is a factor of p(x).