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Verified answer
G (x) = 2x² - xg (x + 1) = 2 (x + 1)² - (x + 1)
g (x + 1) = 2 (x² + 2x + 1) - (x + 1)
g (x + 1) = 2x² + 4x + 2 - x - 1
g (x + 1) = 2x² + 3x + 1