9709 P31 - Jun 2026 - Q10 - 10 marks
9098
The polynomial \(p(x)=ax^3-11x^2+bx+4\), where \(a,b\) are constants, has factor \((x-2)\). When \(p\prime(x)\) is divided by \((x-2)\), the remainder is \(24\).
(a) Find \(a\) and \(b\). [5]
(b)(i) When \(a,b\) have these values, factorise \(p(x)\) completely. [3]
(b)(ii) Hence solve \(p(x)\ge0\). [2]
