# AIME 1986

Algebra Level 4

The polynomial $$1-x+{x}^{2}-{x}^{3}+.....-{x}^{17}$$

may be written in the form $${a}_{0}+{a}_{1}y+{a}_{2}{y}^{2}.....+{a}_{17}{y}^{17}$$

$$where \quad y=x+1$$ and $${a}_{i}s$$ are constant then find $${a}_{2}$$

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