To analyze the polynomial \(-2a^3b^2 + 5ab^5 + 7b^4 + 8\), we can determine the following:
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Degree of the polynomial: The degree of a polynomial is the highest sum of the exponents of the variables in any single term.
- For the term \(-2a^3b^2\), the sum of the exponents is \(3 + 2 = 5\).
- For the term \(5ab^5\), the sum of the exponents is \(1 + 5 = 6\).
- For the term \(7b^4\), the sum of the exponents is \(4\).
- For the constant term \(8\), there are no variables, so the degree is \(0\).
The highest degree among these is \(6\), so the degree of the polynomial is 6.
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Leading coefficient of the polynomial: The leading coefficient is the coefficient of the term with the highest degree, which we identified as \(5ab^5\). The coefficient here is \(5\), so the leading coefficient is 5.
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Constant term of the polynomial: The constant term is the term that does not contain any variables, which in this polynomial is \(8\). Thus, the constant term is 8.
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Leading term of the polynomial: The leading term is the term with the highest degree, which we determined to be \(5ab^5\). Therefore, the leading term of the polynomial is 5ab^5.
To summarize:
- The degree of the polynomial is 6.
- The leading coefficient of the polynomial is 5.
- The constant term of the polynomial is 8.
- The leading term of the polynomial is 5ab^5.