2021 HSC Mathematics Extension 1
Question 3:
Polynomial roots
What is the remainder when is divided by ?
How to recognise this question
Question type: polynomial roots
- The command and notation point to polynomial roots.
- The requested response is a multiple choice.
How to handle it: translate the requested symmetric expression into sums and products of roots from the coefficients.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- By the remainder theorem, the remainder on division by is .
- .
- Option A negates the correct remainder; B and C arise from evaluating at the wrong input or arithmetic slips.
- Answer: D. (NESA multiple-choice key: D.)
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
What is the remainder when is divided by ?
Question 2
What is the remainder when is divided by ?
Question 3
What is the remainder when is divided by ?