If a polynomial is divided by (x+2), the remainder is -19. When
the same polynomial is divided by (x-1), the remainder is 2.
Determine the remainder when the polynomial is divided by
(x-1)(x+2). We know that and where and are two polynomials such
that . Thus, and . The remainer, when dividing by can be of
degree 1 at most since is a polynomial of degree 2. This is, and
where is a polynomial of degree We see that and but we know that
and so we've to solve a linear system of equations in the
unknowns a and b. It's easy to solve this system and the
solution is Therefore, the reaminder when is divided by is