Guṇakasamuccayaḥ — The factors of the sum is the sum of the factors

गुणकसमुच्चयः — Gunakasamuchyah

The factors of the sum is the sum of the factors. The factors of an expression when evaluated at a value equal the expression's value — use this to verify factorizations.

Why it works: If P(x) = (x−a)(x−b), then P(a)=0 and P(b)=0. Evaluating the factors and the original polynomial at any value provides a consistency check on the factorization.

Speed advantage: Instant factorization verification vs. polynomial expansion.

Best for

• Verifying polynomial factorizations

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Originally published at https://www.sutraflow.app/sutras/gunakasamuchyah