To determine the nature of the result of the multiplication problem \((9x^3 + \frac{7}{6})(x - \frac{2}{5})\), we can analyze it step by step.
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Identify the types of expressions involved:
- \(9x^3 + \frac{7}{6}\) is a polynomial (specifically a cubic polynomial).
- \(x - \frac{2}{5}\) is also a polynomial (specifically a linear polynomial).
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Multiplying polynomials:
- The product of two polynomials is always a polynomial. In this case, multiplying a cubic polynomial by a linear polynomial will result in a polynomial of degree \(3 + 1 = 4\).
Given that both parts of the multiplication are polynomials, the result will also be a polynomial.
Thus, the correct option that must be true about the multiplication problem is:
C) The result is a polynomial.