(i)[5]
Determine the values of $a$ and $b$.
(ii)[3]
When $a$ and $b$ take these values, factorise $p(x)$ completely.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
Define $p(x)$ as the polynomial $2x^3 + 5x^2 + ax + b$, with $a$ and $b$ as constants. It is stated that $(2x + 1)$ is a factor of $p(x)$, and that the remainder on dividing $p(x)$ by $(x + 2)$ is $9$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $x=-\frac{1}{2}$, set the expression equal to zero and obtain a correct equation” …
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