2015/069) $P(x)$ is unknown and when divided by $(x+1)(x-3)$ the remainder becomes $2x+7$

What is the remainder when $P(x)$ is divided by $(x-3)$ ?

Solution
Because $P(x)$ divided by $(x+1)(x-3)$ the remainder becomes $2x+7$ so there exists $Q(x)$ such that

$P(x) = Q(x) (x+1)(x-3) + 2x + 7$
so remainder when divided by $x-3$ is using remainder theorem
$P(3) = Q(3) (x+1) 0 + 2 * 3 + 7 = 13$