# Topic Questions: • use the factor theorem and the remainder theorem — 9709 P3 Algebra

> 22 9709 P3 Algebra topic questions (82 marks) on use the factor theorem and the remainder theorem — 15 papers, 2021–2026. Open the exact question in the…

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CIE IAL · Mathematics · 9709 P3 · Algebra

22 9709 P3 Algebra topic questions are tagged to this syllabus point across 15 papers (2021–2026). Only the parts whose knowledge graph matches this syllabus statement are counted, and the table shows which parts of each question are involved.

- 22 topic questions
- 15 papers
- 82 tagged marks
- 14.1% of topic questions
- 14.3% of topic marks
- 2021–2026
- Syllabus 2020–2027
- [All 9709 P3 Algebra topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**This Algebra syllabus point appears in 15 9709 P3 papers across 2021–2026, contributing 22 topic questions and 82 marks.** The most recent appearance is 9709/31 May/June 2026. That equals 14.1% of the 156 topic questions and 14.3% of the 573 marks tagged to Algebra. Only parts tagged to this subtopic are counted, so a four-part question can contribute one item and one part's marks. The table lists every matching question, its tagged parts and marks, with a link back to the paper page. Sessions are newest first, so the statement can be traced back through the full paper history.

## Topic questions by session

Newest sessions first. Parts and marks count only the parts tagged to this subtopic; “x of y parts” shows how much of the question is tagged elsewhere. Select the paper cell to open the matching question on the paper page, or use **Go to Practice Hub** to answer that exact question in the Interactive Practice Hub.

| Paper | Question | Type | Parts | Marks | Difficulty | Practice |
| --- | --- | --- | --- | --- | --- | --- |
| [**9709/31** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-may-june-9709-31/#q-10) | **Q10** Polynomial Factor and Remainder Theorem - CIE Pure Mathematics 2026 Q10 | FRQ | 3 parts ((a), (b)(i), (b)(ii)) | 10 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=5a21f0d9-d2ad-4ffc-9254-eb21daddd8fc&question_id=48d45c7a-4a78-4911-93ba-412861a5e4cb&source_detail=9709%2F31+May%2FJune+2026) |
| [**9709/32** March 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-march-9709-32/#q-6) | **Q6** Polynomial Factorisation and Division - CIE P3 2026 Mar Q6 | FRQ | 2 parts ((a), (b)) | 6 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0fd758f5-8815-4e29-a05d-65b87156efed&question_id=59a37f7a-5e5d-46cc-8e3a-a8f5a1984842&source_detail=9709%2F32+March+2026) |
| [**9709/32** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-32/#q-5) | **Q5** Repeated Factor Theorem and Polynomial Differentiation - CIE A Level Maths 2025 Winter P32 Q5 | FRQ | 2 parts ((a), (b)) | 7 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d271f67a-f544-4649-81c5-cdf7c8a90ccc&question_id=a59a1044-ff98-421b-9d12-62b219828c95&source_detail=9709%2F32+October%2FNovember+2025) |
| [**9709/31** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-may-june-9709-31/#q-5) | **Q5** Polynomial Remainder Theorem with Parameters - CIE Pure Mathematics 2025 Jun Paper 31 Q5 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d305e649-31d7-4036-b6fa-6295b81b011f&question_id=f513d609-414e-4bbd-96ab-e669fa89347c&source_detail=9709%2F31+May%2FJune+2025) |
| [**9709/32** March 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-march-9709-32/#q-9) | **Q9** Factor Theorem and Polynomial Inequality - CIE A-Level Math 2025 Mar Paper 32 Q9 | FRQ | 2 of 3 parts ((a), (b)) | 8 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ebe23b18-f2b2-4e16-8e60-c5ac5649cb15&question_id=17388a77-7be5-4b6c-b386-aea867d66a6d&source_detail=9709%2F32+March+2025) |
| [**9709/31** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-october-november-9709-31/#q-1) | **Q1** Polynomial Factor and Remainder Theorem - CIE A-Level Maths 2024 Nov Paper 31 Q1 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=70a34762-5adb-4bbc-a073-ccdcbf562e7c&question_id=fb49cd2d-be97-4421-bf0a-67d963fca3e8&source_detail=9709%2F31+October%2FNovember+2024) |
| [**9709/33** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-may-june-9709-33/#q-7) | **Q7** Polynomial Factorization and Trigonometric Equation - CIE A-Level Pure Mathematics | FRQ | 1 of 3 parts ((a)) | 1 of 6 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7e0feb6b-4f09-4f55-8eeb-a9c09d82ec52&question_id=f8a32917-41dd-4e1c-88ce-d2d3ccf7fd60&source_detail=9709%2F33+May%2FJune+2024) |
| [**9709/32** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-october-november-9709-32/#q-3) | **Q3** Polynomial Factor and Remainder Theorem - CIE 9709 2023 Nov Paper 32 Q3 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=3fb73dde-04cc-4e60-91c5-1ddfee06f24d&question_id=535016b7-35ef-4a81-ab02-70e023762e6e&source_detail=9709%2F32+October%2FNovember+2023) |
| [**9709/33** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-october-november-9709-33/#q-3) | **Q3** Polynomial Remainder Theorem - CIE A-Level Maths 2023 Q3 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=719f9f72-ffe6-4873-b35f-05b84c1bcd86&question_id=d0c89738-807f-4dcf-8d0d-732d58a055ad&source_detail=9709%2F33+October%2FNovember+2023) |
| [**9709/31** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-may-june-9709-31/#q-10) | **Q10** Polynomial Roots and Complex Numbers - CIE Pure Mathematics 2023 Q10 | FRQ | 1 of 3 parts ((a)) | 2 of 12 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cfca2669-2cc1-43c6-a0cc-6132556376c3&question_id=93030561-ce67-4186-ba2f-881a8ef6c8c0&source_detail=9709%2F31+May%2FJune+2023) |
| [**9709/32** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-october-november-9709-32/#q-2) | **Q2** Factor Theorem and Polynomial Inequality - CIE Pure Mathematics 2022 Nov Paper 32 Q2 | FRQ | 2 parts ((a), (b)) | 6 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ec345ecb-a979-44f7-9e14-294a778ff934&question_id=bc9e5d28-4d69-46f0-878a-5f000eb5fec7&source_detail=9709%2F32+October%2FNovember+2022) |
| [**9709/31** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-may-june-9709-31/#q-5) | **Q5** Repeated Factors of Polynomial - CIE Pure Mathematics 2022 Jun Paper 31 Q5 | FRQ | 2 parts ((a), (b)) | 8 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=09685b56-86ca-46e2-9c33-353cef143122&question_id=b324d271-99d4-4708-a315-7a25cc49881c&source_detail=9709%2F31+May%2FJune+2022) |
| [**9709/32** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-may-june-9709-32/#q-3) | **Q3** Polynomial Remainder Theorem - CIE Mathematics 2022 Jun Q3 | FRQ | 1 part | 5 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6ad396ce-ab9f-4c82-bba2-087b907a1ea1&question_id=70d01e1c-c3f5-49f6-8cb1-534467d78319&source_detail=9709%2F32+May%2FJune+2022) |
| [**9709/32** October/November 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-october-november-9709-32/#q-11) | **Q11** Curve Gradient and Iterative Root Finding - CIE A-Level Mathematics 2021 Nov Paper 32 Q11 | FRQ | 1 of 3 parts ((b)) | 4 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e143fbb0-4c0c-42bd-8875-d51f745a2eeb&question_id=c0df5c26-0db9-4ef5-af56-698006ddc81f&source_detail=9709%2F32+October%2FNovember+2021) |
| [**9709/32** March 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-march-9709-32/#q-2) | **Q2** Polynomial Factor and Remainder Theorem - CIE A-Level Mathematics 2021 March Paper 32 Q2 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ab7133da-61cb-4438-b5f6-ad6909bb250e&question_id=c47fb6bf-9cd6-4226-b65a-c96b2e6f4e3b&source_detail=9709%2F32+March+2021) |

## Related topic questions in Algebra

- [• divide a polynomial, of degree not exceeding 4, by a linear or quadratic polynomial, and identify the quotient and remainder (which may be zero)](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/divide-a-polynomial-of-degree-not-exceeding-4-by-a-linear-or-quadratic-polynomial-and/) — 24 question items · 21 papers — 82 marks · 2020–2026
- [• recall an appropriate form for expressing rational functions in partial fractions, and carry out the decomposition, in cases where the denominator is no more complicated than – $(ax+b)(cx+d)(ex+f)$ – $(ax+b)(cx+d)^2$ – $(ax+b)(cx^2+d)$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/recall-an-appropriate-form-for-expressing-rational-functions-in-partial-fractions-and/) — 36 question items · 34 papers — 178 marks · 2020–2026
[**• understand the meaning of $|x|$, sketch the graph of $y=|ax+b|$ and use relations such as $|a|=|b|\Leftrightarrow a^2=b^2$ and $|x-a|** 32 question items · 23 papers 88 marks · 2020–2026](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/understand-the-meaning-of-x-sketch-the-graph-of-y-ax-b-and-use-relations-such-as-a-b/)
[**• use the expansion of $(1+x)^n$, where $n$ is a rational number and $|x|<1$** 32 question items · 22 papers 107 marks · 2020–2026](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/use-the-expansion-of-1-x-n-where-n-is-a-rational-number-and-x-1/)

## Topic question rules and edge cases

**How many topic questions cover this syllabus point?**

15 question stems cover this subtopic across 15 papers, but only 22 tagged parts and 82 marks belong to it. Other parts of the same questions are assessed under different statements and are excluded from this page.

**Which papers include this subtopic?**

The table lists every matching session from 2021–2026. Each row links to the question anchor on the paper page, where the full paper context and practice entry point are available.

**Why can one question appear under several subtopics?**

The parts of one question can assess different syllabus statements. Each part is counted under its own subtopics, so the same question stem can appear on several subtopic pages while each page lists only the parts and marks tagged to that statement.

**Can I practise these questions with AI marking?**

Yes. Open a paper from the table and use the Interactive Practice Hub entry point. The page itself is static HTML so search engines and retrieval agents can read the full question list without executing JavaScript.

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