Mathematics (AS & A Level) · May / June 2025 · Paper 31 · Question 5

The polynomial x pax a x qa 3 7 3 2 2 3 + + + is denoted by ( )x f , where p, q and a are constants and a 0 ! . When ( )x f is divided by ( ) x a 2 + the remainder is a 22 3 - . When ( )x f is divided by ( ) x a 3 - the remainder is a3 - . Find the values of p and q. [5]

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