SEARCH HOME
 Math Central Quandaries & 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)?

Hi,

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,
Penny

Math Central is supported by the University of Regina and the Imperial Oil Foundation.