Kenneth ChengMathematical modeling
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Recover f(−2) using the cancellation of odd powers.

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TOPIC 01

2026 JM01

Do not assume a polynomial with mixed powers is odd.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

Recover f(−2) using the cancellation of odd powers.

f(x)=ax3−8x2+bx−4,f(2)=−6f(x)=ax^3-8x^2+bx-4,\quad f(2)=-6

Official paper · jm01-2026 · I.9 · PDF 3

Official original and suggested answers ↗ · Suggested answer PDF page 6

Skills and prerequisite lessons
  1. Option A66
  2. Option B3636
  3. Option C6666
  4. Option D−36-36
  5. Option E−66-66

Working and explanation

BUILD THE REASONING

Hint 1
Add f(x) and f(−x).
Hint 2
The terms involving a and b cancel.
Worked solution

  1. Only the even-power and constant terms remain.

    f(x)+f(−x)=−16x2−8f(x)+f(-x)=-16x^2-8

  2. Evaluate the identity at x=2.

    −6+f(−2)=−72  ⟹  f(−2)=−66-6+f(-2)=-72\implies f(-2)=-66

E: −66.

Checks and common pitfalls: Do not assume a polynomial with mixed powers is odd.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Only the even-power and constant terms remain.
    f(x)+f(−x)=−16x2−8f(x)+f(-x)=-16x^2-8
  • Evaluate the identity at x=2.
    −6+f(−2)=−72  ⟹  f(−2)=−66-6+f(-2)=-72\implies f(-2)=-66

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