(i)[5]
Determine the values of $a$ and $b$.
(ii)[3]
With these values of $a$ and $b$, fully factorise $p(x)$.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
The polynomial $ax^3 - 3x^2 - 11x + b$, with $a$ and $b$ as constants, is written as $p(x)$. It is stated that $(x + 2)$ divides $p(x)$ exactly, and that the remainder when $p(x)$ is divided by $(x + 1)$ is $12$.
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This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $x = -2$, make the expression equal to zero and produce a correct equation in any form” …
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