To perform the operation \((-4x^2 + 6x + 1) + (5x + 7)\), we will combine like terms.
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Start by distributing and grouping the terms: \[ -4x^2 + 6x + 1 + 5x + 7 \]
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Combine the \(x\) terms: \[ 6x + 5x = 11x \]
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Combine the constant terms: \[ 1 + 7 = 8 \]
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Therefore, the expression can be rewritten as: \[ -4x^2 + 11x + 8 \]
Thus, the final result is: \[ -4x^2 + 11x + 8 \]