Question

The polynomial x^3 +3x^2 -2x -1 leaves a remainder of 3 when divided by (x+1) and a remainder of 15 when divided by (x-2). Find the remainder when it is divided by (x-2)(x+1).

Answer 1

\[x^3 +3x^2 -2x -1\]

Answer 2

is there a snap way of doing this without simply dividing? your remainder will be a polynomial of degree 1

Answer 3

It says you need to divide...

Answer 4

I don't see how to use the remainders to "jump" to the answer. But one way to find the remainder is expand (x-2)(x+1) = x^2-x-2
now divide this into the original expression.
If you know synthetic division, you can use that.

Answer 5

Here's how to do the division (if you are rusty at it)
http://www.khanacademy.org/video/algebraic-long-division?playlist=Algebra