Polynomial roots — Identity practice

Question

For with roots , prove .

This practice question was inspired by Question 13(d) in the 2022 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

State the final answer clearly in the form the question requested.Expand as above using and .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Key lemma for the original problem.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.