0606 P11 - Jun 2024 - Q2 - 6 marks
7296
DO NOT USE A CALCULATOR IN THIS QUESTION. The polynomial p is such that \(\mathrm{p}(x)=6 x^{3}-35 x^{2}+34 x+45\). (a) Find \(\mathrm{p}(x)\) in the form \((2 x-5) \mathrm{q}(x)+r\), where \(\mathrm{q}(x)\) is a polynomial and \(r\) is a constant. (b) Hence write the expression \(\mathrm{p}(x)-5\) as a product of linear factors. (c) Hence write down the solutions of the equation \(\mathrm{p}(x)=5\).
