(i)[5]
Determine the values of $a$ and $b$.
(ii)[2]
When $a$ and $b$ take these values, determine the greatest possible value of $g(x) - f(x)$ as $x$ changes.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The polynomials $f(x)$ and $g(x)$ are given by $f(x) = x^3 + ax^2 + b$ and $g(x) = x^3 + bx^2 - a$, where $a$ and $b$ are constants. It is known that $(x + 2)$ is a factor of $f(x)$. It is also known that, after $g(x)$ is divided by $(x + 1)$, the remainder is $-18$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Put $x=-2$ into $f(x)$ and set it equal to zero to get $-8+4a+b=0$ or an equivalent result” …
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