The polynomial leaves the same remainder when divided by and

MATHEMATICS · Single correct · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1

Problem

The polynomial

f(x)

leaves the same remainder when divided by

(x-1)

and

(x+1)

. Which of the following must hold? (a)

(x-1)(x+1)

is a factor of

f(x)

(b)

f(1)+f(-1)=0

(c)

f(1)=f(-1)

(d) The degree of

f(x)

is even