To analyze the multiplication problem \((\frac{9x^3 + 7}{6})(\frac{x - 2}{5})\), we need to consider the nature of the expressions involved.
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Identifying the expressions:
- The first part, \(9x^3 + 7\), is a polynomial.
- The second part, \(x - 2\), is also a polynomial.
- Both fractions have constants in the denominator (6 and 5), but they don't affect the polynomial nature of the numerator.
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Multiplying the expressions: When you multiply two polynomials, the result is still a polynomial. Therefore, after performing the multiplication, the resulting expression will still be a polynomial (even after dividing by constants).
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Closed systems: A "closed system" in this context typically refers to whether operations (like addition or multiplication) yield results that stay within a defined set of values (like integers or real numbers). The result of the multiplication here will remain within the realm of polynomials.
Given this understanding, the correct response is:
The result is a polynomial.