1. ## Polynomial help

The polynomial P(x) has remainder 1 when divided by (x-1) , and remainder 3 when divided by (x+1) . Find the remainder when P(x) is divided by $\displaystyle (x^2-1)$.

The polynomial P(x) has remainder 1 when divided by (x-1) , and remainder 3 when divided by (x+1) . Find the remainder when P(x) is divided by $\displaystyle (x^2-1)$.
P(x) = Q(x) (x - 1)(x + 1) + (ax + b) where Q(x) is a polynomial.

When P(x) is divided by $\displaystyle (x^2-1)$ the remainder is ax + b.

Now note:

P(1) = 1 => 1 = a + b .... (1)

P(-1) = 3 => 3 = -a + b .... (2)

Solve equations (1) and (2) simultaneously.