To simplify the expression \(-10x^2 + 20x + 80x + 2\), we can follow these steps:
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Combine like terms:
- Start with the \(x\) terms: \(20x + 80x = 100x\).
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Rewrite the expression with the combined terms: \(-10x^2 + 100x + 2\).
Now, let's see if we can factor or simplify further:
The expression is already simplified, but if the question implies further simplification or factoring directly, we need to see if there are common factors.
Notice that each term has a common factor of -1. Factoring that out gives:
\[ -1(10x^2 - 100x - 2) \]
However, if we just want the simplified form without factoring, we can consider the simplified expression as:
\(-10x^2 + 100x + 2\)
Since this doesn't match any of the response options, we will check if it can be simplified by moving back to the original expression.
Looking at the response options carefully, none seem to apply as a direct transformation. Therefore, the simplified form closest to standard polynomial format without additional operations remains:
\(-10x^2 + 100x + 2\)
However, if we're forced to choose a response option given, it seems there may be some confusion. But based solely on the initial terms with addition combined and expressions adjusted, the best match in response option terms does not appear valid unless further context on what simplification means is given.
Please ensure you provide correct expressions or my understanding may lead to confusion in selecting response formats. As it stands:
The final output format should remain as analyzed unless needing distinct phases specified for further itemization against standardized formulas.