Exam-style question
Try this first
After dividing a cubic polynomial by (x + 1), what should the final answer include?.
- A.B6: connect the result back to the original question
- B.Use any familiar GCSE calculation even if it ignores Manipulate polynomials algebraically
- C.Write only the final answer without showing the mathematical method
- D.Change the notation or restrictions to make the algebra look simpler
Model answer
What a good answer should say
- The correct answer is B6: connect the result back to the original question.
- The answer should state the quotient and remainder, or confirm exact divisibility if the remainder is zero.
This answer is tied to the objective: B6 Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use the factor theorem; simplify rational expressions including by factorising and cancelling, and algebraic division by linear expressions only..
Explanation
Why this works
Use the explanation to connect the worked answer back to B6 Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use the factor theorem; simplify rational expressions including by factorising and cancelling, and algebraic division by linear expressions only..
The correct option, B6: connect the result back to the original question, is supported because algebraic division by a linear expression is complete only when the quotient and remainder are interpreted. A zero remainder confirms a factor; a non-zero remainder means the division is not exact.
The distractors are weaker because they stop at partial working or ignore the remainder.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: analysis.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.