Variation 2 · answer guide

Polynomial roots — Divisor x+1

Question

What is the remainder when is divided by ?

This practice question was inspired by Question 3 in the 2021 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: translate the requested symmetric expression into sums and products of roots from the coefficients..
Finish the calculation, then check that the result meets the question’s conditions.Evaluating at incorrectly gives (option C).
Match the result to the choices and state the correct option.Therefore option A is correct.

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

Verification: Remainder theorem uses the root of the divisor: .

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