2026 ZHSS P2 Q2

Secondary 4

8 marks

It is given that \(f(x)=2x^3-17x^2+41x-30\).
Show that \((2x-3)\) is a factor of \(f(x)\).[1]
Express \(f(x)\) as a product of three linear factors.[3]
Hence, solve \(f(x)=0\).[1]
Information about another function \(g(x)\) is given below.
1. \(g(x)\) gives a remainder of 2 when divided by \((x-3)\).
2. \(g(x)\) gives a remainder of 2 when divided by \((3x-1)\).
3. \(g(x)\) is a quadratic function.
Suggest a possible function for \(g(x)\) in the form \(ax^2+bx+c\).[2]
Factorise \(x^6+27y^3\).[1]

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Answer:(a) Factor shown. (b) \((2x-3)(x-2)(x-5)\) (c) \(x=\dfrac32,2,5\) (d) For example, \(g(x)=3x^2-10x+5\). (e) \((x^2+3y)(x^4-3x^2y+9y^2)\)

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