Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

(i)[2]

The polynomial $f(x)$ can be expressed in the form $(x - 2)^2 g(x)$, where $g(x)$ is another polynomial. Show that $(x - 2)$ is a factor of $f'(x)$.

(ii)[5]

The polynomial $x^5 + ax^4 + 3x^3 + bx^2 + a$, where $a$ and $b$ are constants, has $(x - 2)^2$ as a factor. Using the factor theorem and the result of part (i), or otherwise, find the values of $a$ and $b$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Differentiate $f(x)$, giving $f'(x)=(x-2)^2g'(x)+2(x-2)g(x)$

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