When the polynomial $3{x^3} + ax + b$ is divided by $(x - 2)$, the remainder is 2, and when divided by $(x + 1)$, it is 5. Find the value of a and the value of b.

$P(2) = 24 + 2a + b = 2,{\text{ }}P( - 1) =  - 3 - a + b = 5$     M1A1A1

$(2a + b =  - 22,{\text{ }} - a + b = 8)$

Note:     Award M1 for substitution of 2 or −1 and equating to remainder, A1 for each correct equation.

attempt to solve simultaneously     M1

$a =  - 10,{\text{ }}b =  - 2$     A1

[5 marks]