In Q[x], coefficient vectors are ordered from lowest to highest power. Add [1, 2] and [-1]. Return the coefficient vector with trailing zeros removed, representing the zero polynomial by [0].
G001 — In Q[x], coefficient vectors are ordered from lowest to highest power. Add [1, 2] and [-1]. Return the coefficient vector with trailing zeros removed, representing the zero polynomial by [0].
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.
Check THIS bank’s keys/operation/domain:legacy table underscores,MOD50 local hyphens;permissive BASE data acquires no unknown-field restriction.Keep Number.isInteger and SAFE source guards distinct,while preserving ORIGINAL JSON number representations.
In Q[x],coefficients run from low to high degree.Type EVERY RAW SAFE cell of a0..32-entry list,including trailing zeros.Trim ONLY trailing zeros,not internal zeros.The zero polynomial has empty internal support but displays[0];keep the ORIGINAL source vector unchanged.
In Q[x],coefficients run from low to high degree.Type EVERY RAW SAFE cell of a0..32-entry list,including trailing zeros.Trim ONLY trailing zeros,not internal zeros.The zero polynomial has empty internal support but displays[0];keep the ORIGINAL source vector unchanged.
Polynomial ORIGINAL matching-power coefficient0 := sum(1, -1)
After
Polynomial ORIGINAL matching-power coefficient0 = 0
Conditions: none
Calculate exactly from ORIGINAL ordered operands.Legacy derived integers are not recapped at the RAW SAFE bound;MOD50 rationals separately retain the NAIVE pre-reduction source envelope.
Polynomial ORIGINAL matching-power coefficient1 := sum(2, 0)
After
Polynomial ORIGINAL matching-power coefficient1 = 2
Conditions: none
Calculate exactly from ORIGINAL ordered operands.Legacy derived integers are not recapped at the RAW SAFE bound;MOD50 rationals separately retain the NAIVE pre-reduction source envelope.
Add EVERY matching power,using0 only outside support,THEN trim trailing zeros.Full cancellation displays[0].ALL coefficients determine the polynomial sum,not one sampled value.Derived coefficient sums may exceed RAW SAFE.
S006 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
S005 · premise_and_result_audit — Recompute Polynomial ORIGINAL matching-power coefficient1 with exact rational arithmetic, not rounded decimals.
S004 · premise_and_result_audit — Recompute Polynomial ORIGINAL matching-power coefficient0 with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
S002 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
S001 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
Result
[0, 2]
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.