9709 P21 - Jun 2022 - Q7 - 9 marks
10373
The polynomial \(p(x)\) is defined by \[p(x)=2x^3+5x^2+ax+2a,\] where \(a\) is an integer.
(a) Find, in terms of \(x\) and \(a\), the quotient when \(p(x)\) is divided by \((x+2)\), and show that the remainder is 4. [3]
(b) It is given that \[\int_{-1}^1\frac{p(x)}{x+2}\,dx=\frac{22}3+\ln b,\] where \(b\) is an integer. Find the values of \(a\) and \(b\). [6]
