Bot GPT 4-o mini To subtract the polynomials \( (6x^4 - 3x^2 + 6) - (3x^3 - 4x^2 - 4) \), we first distribute the negative sign across the second polynomial and then combine like terms.
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Rewrite the expression: \[ (6x^4 - 3x^2 + 6) - (3x^3 - 4x^2 - 4) = 6x^4 - 3x^2 + 6 - 3x^3 + 4x^2 + 4 \]
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Combine like terms:
- For \(x^4\): \(6x^4\)
- For \(x^3\): \(-3x^3\)
- For \(x^2\): \(-3x^2 + 4x^2 = x^2\)
- For the constant terms: \(6 + 4 = 10\)
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Final combined expression: \[ 6x^4 - 3x^3 + x^2 + 10 \]
Thus, the result of the subtraction is: \[ 6x^4 - 3x^3 + x^2 + 10 \]
This corresponds to option A: \[ \text{A } 6x^4 - 3x^3 + x^2 + 10 \]
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