JAMB 1998 · UME · Q10

Polynomials & algebraic division

When the expression $pm^2 + qm + 1$ is divided by $(m - 1)$ the remainder is 2, and when divided by $(m + 1)$ the remainder is 4. Find $p$ and $q$ respectively.

Worked solution (try it first)

By the remainder theorem, dividing by $m - 1$ leaves the value at $m = 1$ : $p + q + 1 = 2$ , so $p + q = 1$ .
Dividing by $m + 1$ leaves the value at $m = -1$ : $p - q + 1 = 4$ , so $p - q = 3$ .
Add the equations: $2p = 4$ , so $p = 2$ and $q = -1$ , option A.

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