Exam-style question
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B6: A student divides p(x) by (x - 3) and obtains quotient x^2 + 2x - 1 with remainder 5. Explain what this means about p(x).
Model answer
What a good answer should say
- The division result means p(x) = (x - 3)(x^2 + 2x - 1) + 5.
- Because the remainder is 5, (x - 3) is not a factor of p(x).
- A complete answer should name the quotient, state the remainder, and explain that exact divisibility would require a zero remainder.
- The common error is to quote the quotient only and ignore what the remainder says about the factor theorem.
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..
This B6 question is specific to polynomial division because it interprets quotient, remainder and exact divisibility by a linear expression.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: exam_style.
- Reasoning demand: recall.
- 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.