Math CentralQuandaries & Queries


Question from Pratyasha, a student:

A quadratic polynomial when divide by x+2 leaves a remainder of 1 and when divided by x-1 leaves a
remainder of 4. What will be the remainder if it is divided by (x+2)(x-1)?


I can help get you started.

Suppose your quadratic polynomial is $f(x).$ Since $(x + 2)(x - 1)$ is a quadratic polynomial the remainder after dividing $f(x)$ by $(x + 2)(x - 1)$ must be a linear polynomial which means that there is a polynomial $g(x)$ and numbers $a$ and $b$ so that

\[ f(x) = g(x) (x + 2)(x - 1) + ax + b.\]

Can you complete the problem now? Write back if you need more assistance,

About Math Central


Math Central is supported by the University of Regina and the Imperial Oil Foundation.
Quandaries & Queries page Home page University of Regina