To find the sum of the two polynomials \((-8x^2 - 10x + 7)\) and \((-9x^2 - 3)\), we will combine like terms.
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Write down the polynomials: \[ (-8x^2 - 10x + 7) + (-9x^2 - 3) \]
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Combine like terms:
- For the \(x^2\) terms: \(-8x^2 - 9x^2 = -17x^2\)
- For the \(x\) terms: \(-10x\) (there's no other \(x\) term to combine with, so it remains \(-10x\))
- For the constant terms: \(7 - 3 = 4\)
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Put it all together: \[ -17x^2 - 10x + 4 \]
Thus, the sum of the polynomials is: \[ \boxed{-17x^2 - 10x + 4} \]
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