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Polynomials add term by term: line the coefficients up by power and add. Missing powers count as zero, which is why the shorter list is padded on the left.
Polynomial addition
(Σaₖxᵏ) + (Σbₖxᵏ) = Σ(aₖ + bₖ)xᵏ
3x³ + x² + 2x + 7.
If the leading terms cancel, as in (x² + 1) + (−x² + 3), the degree falls — here to zero.