(i)[5]
Determine the values of $a$ and $b$.
(ii)[2]
With these values of $a$ and $b$, determine the quadratic factor of $p(x)$.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
The polynomial $ax^3 + bx^2 + 5x - 2$, with $a$ and $b$ as constants, is written as $p(x)$. It is known that $(2x - 1)$ is a factor of $p(x)$, and that dividing $p(x)$ by $(x - 2)$ leaves a remainder of $12$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $x=\tfrac12$ and make the expression equal to zero, or carry out the division, and then write down a correct equation” …
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