Bot GPT 4-o mini To find the highest degree of the expression \((3x^2 + 4)(x^5 - 3) - 12x^9 - 24x^3x + 2\), we can break it down into parts.
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Calculate the degree of \((3x^2 + 4)(x^5 - 3)\):
- The first expression \(3x^2 + 4\) has a degree of 2 (highest power of \(x\) is \(2\)).
- The second expression \(x^5 - 3\) has a degree of 5.
- The degree of the product \((3x^2 + 4)(x^5 - 3)\) is \(2 + 5 = 7\).
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Identify the degrees of the other terms:
- The term \(-12x^9\) has a degree of 9.
- The term \(-24x^3x\) can be simplified to \(-24x^4\) (adding the powers of \(x\)), which has a degree of 4.
- The constant term \(+2\) is degree 0.
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Compare the degrees:
- From \((3x^2 + 4)(x^5 - 3)\), we have degree 7.
- The term \(-12x^9\) gives degree 9.
- The term \(-24x^4\) gives degree 4.
- The constant \(+2\) gives degree 0.
The highest degree among these is from the term \(-12x^9\), which has degree 9.
Thus, the highest degree of the entire expression is 9.
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