Paper 1 · remainder theorem

A polynomial $f(x)$ leaves remainder $-9$ when divided by $(x-3)$ and remainder $-6$ when divided by $(2x-1)$ . Find the remainder when $f(x)$ is divided by $(x-3)(2x-1)$ .

-\tfrac{6}{5}x - \tfrac{27}{5}

\tfrac{6}{5}x - \tfrac{27}{5}

-\tfrac{27}{5}x - \tfrac{6}{5}

-15

Explanation: Write

f(x)=(x-3)(2x-1)Q(x)+ax+b

. Then

3a+b=-9

and

\tfrac12a+b=-6

. Solving gives

a=-\tfrac65

b=-\tfrac{27}{5}

Derived from ZIMSEC Mathematics Paper 1, November 2015, Q1

Get the full paper, not just one question

Danho has every sitting for this paper, with your progress tracked question by question, offline.