Bot GPT 4-o mini To determine the first and last terms of the expression \((12x^5 + 4x^4 + 9x^3 - 10x^2 + 15) - (24x^5 + 9x^3 - 7x^2 + 8)\), we need to simplify the expression.
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Distribute the negative sign across the second set of parentheses: \[ 12x^5 + 4x^4 + 9x^3 - 10x^2 + 15 - 24x^5 - 9x^3 + 7x^2 - 8 \]
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Combine like terms:
- For \(x^5\) terms: \(12x^5 - 24x^5 = -12x^5\)
- For \(x^4\) terms: \(4x^4\) (there's no other x^4 term)
- For \(x^3\) terms: \(9x^3 - 9x^3 = 0\)
- For \(x^2\) terms: \(-10x^2 + 7x^2 = -3x^2\)
- For the constant terms: \(15 - 8 = 7\)
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Now write the simplified expression: \[ -12x^5 + 4x^4 - 3x^2 + 7 \]
From this result:
- The first term (the term with the highest degree) is \(-12x^5\).
- The last term (the constant term) is \(7\).
Thus, the correct response is: The first term is −12x^5, and the last term is 7.
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