2024 IGCSE Additional Mathematics May/June 0606/11 Q2

DO NOT USE A CALCULATOR IN THIS QUESTION.

The polynomial \(\mathrm{p}\) is such that \(\mathrm{p}(x)=6x^3-35x^2+34x+45\).

1. Find \(\mathrm{p}(x)\) in the form \((2x-5)\mathrm{q}(x)+r\), where \(\mathrm{q}(x)\) is a polynomial and \(r\) is a constant.[3]
2. Hence write the expression \(\mathrm{p}(x)-5\) as a product of linear factors.[2]
3. Hence write down the solutions of the equation \(\mathrm{p}(x)=5\).[1]