Exam-style question
Try this first
Why does f(2) = 0 show that (x - 2) is a factor of a polynomial f(x)?.
- A.B6: justify each step using the relevant algebra and functions rule
- 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: justify each step using the relevant algebra and functions rule.
- By the factor theorem, f(a) = 0 means (x - a) is a factor, so f(2) = 0 proves that (x - 2) divides the polynomial exactly.
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: justify each step using the relevant algebra and functions rule, is supported because the factor theorem links a zero of the polynomial to a linear factor. This is not just substitution; the zero remainder proves exact divisibility by x - 2.
The distractors fail because they do not connect f(2) = 0 to the factor theorem.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: understanding.
- 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.