HKDSE (Hong Kong) · Mathematics Compulsory Part

Functions and Polynomials

6 practice questions, each with the answer and an explanation.

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All 6 questions

Let $P (x) = 2 x^{3} - 3 x^{2} + 4 x - 5$ . Find the remainder when $P (x)$ is divided by $x - 2$ .
If $x - 1$ is a factor of $f (x) = x^{3} + k x^{2} - 4 x + 2$ , find the value of $k$ .
Find the coordinates of the vertex of the parabola $y = - 2 x^{2} + 8 x - 5$ .
For what values of $k$ does the quadratic equation $x^{2} - k x + 9 = 0$ have two distinct real roots?
Solve the logarithmic equation $lo g_{3} (x + 2) + lo g_{3} (x - 4) = 3$ .
The graph of $y = f (x)$ has a maximum point at $(4, 6)$ . What are the coordinates of the corresponding maximum point on the graph of $y = 3 f (2 x - 6) - 5$ ?

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