# Question 4202: Complete Polynomial Sum Coefficients

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0007-04202 · q-20261008-advance-20261010-r01-polynomial-0002



## Original question and givens

Integer polynomials have ascending coefficients f=[2] and g=[-3], constant term first. Give the complete ascending coefficient list for f+g.


- G001 — Integer polynomials have ascending coefficients f=[2] and g=[-3], constant term first. Give the complete ascending coefficient list for f+g.





## Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.


- [mko-polynomial](https://ocme.evemisslab.com/en/mko/mko-polynomial/)





## Step-by-step derivation

S001 · impliesBefore

f ascending coefficients=[2]

After

coefficient k multiplies x^k;keep all required degrees

Conditions: none

Coefficients are in ascending powers with the constant at index0.Full coefficient operations are not identities inferred from one-point agreement;retain the original coefficient list.

Step identifiers and dependenciesRule: ascending_polynomial_identity · Uses: G001





S002 · calculationBefore

sum coefficient0 := sum(2, -3)

After

sum coefficient0 = -1

Conditions: none

Combine coefficients of the same power,padding a missing term with0.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S001





S003 · impliesBefore

[-1]

After

canonical ascending coefficient list

Conditions: none

Coefficientwise addition preserves the polynomial identity;remove trailing zeros but retain[0] for the zero polynomial.

Step identifiers and dependenciesRule: polynomial_sum_coefficients · Uses: G001, S002









## Reverse checks


- S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S002 · premise_and_result_audit — Recompute sum coefficient0 with exact rational arithmetic, not rounded decimals.
- S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.





## Result

[-1]

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.





## This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: 0cf1bf20bb67af38185f467cbd6f47e25f950f7bdbe0ec69227ef21ad1a18371
- candidate record SHA-256: 5d5c3198aac5a00bbee2e6851e9a7c154d0eae6e0846641a4923b78f6571f0a8
- semantic review receipt SHA-256: faf0582c0184613e6fae207374056133eae600883a29c67d8438113bbe3c485a
- question-first witness SHA-256: 4b283b6ff424b1d22caa36f3552b0fa21b1b66a0a883d7cbe9cedc8dd77b2e42
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261008-advance-20261010-r01-polynomial-0002.json)