To simplify the polynomial expression \( 7x^2 + 2x - 9 + (x+2)(x-3) \), we will start by simplifying the product \( (x + 2)(x - 3) \).
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Expand the expression \( (x + 2)(x - 3) \): \[ (x + 2)(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6 \]
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Substitute this back into the original expression: \[ 7x^2 + 2x - 9 + (x^2 - x - 6) \]
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Combine like terms:
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First, group all the \(x^2\) terms: \[ 7x^2 + x^2 = 8x^2 \]
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Next, combine the \(x\) terms: \[ 2x - x = x \]
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Finally, combine the constant terms: \[ -9 - 6 = -15 \]
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Write the final simplified expression: \[ 8x^2 + x - 15 \]
Thus, the simplified form of the polynomial expression is: \[ \boxed{8x^2 + x - 15} \]