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).

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- Jan 7th 2010, 05:22 PMshane99Dividing polynomials
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).

- Jan 8th 2010, 01:24 AMDavidEriksson
Hi!

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