To analyze the multiplication problem \((9x^3+76)(x−25)\), we can determine the nature of the result based on the expression itself.
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Identifying the Components:
- The expression \(9x^3 + 76\) is a polynomial of degree 3 (since the highest exponent of \(x\) is 3).
- The expression \(x - 25\) is a polynomial of degree 1.
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Polynomial Multiplication:
- When we multiply two polynomials together, the resulting expression is also a polynomial. The degree of the resulting polynomial is the sum of the degrees of the two polynomials. In this case, the degree will be \(3 + 1 = 4\).
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Conclusion:
- Therefore, the result of the multiplication \((9x^3+76)(x−25)\) will be a polynomial.
Given the options:
- The correct response is: The result is a polynomial.