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Determine $a$ and $b$.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
Let p(x) represent the polynomial $4x^3 + ax^2 + 5x + b$, where $a$ and $b$ are constants. It is stated that $(2x + 1)$ is a factor of $p(x)$. In addition, when $p(x)$ is divided by $(x - 4)$, the remainder is 3 times the remainder obtained when $p(x)$ is divided by $(x - 2)$.
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This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Replace $x$ with $-\tfrac12$ and set the expression equal to zero.” …
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