Question

What must be true about this multiplication problem?

(9x^3+7/6)(x−2/5)

(1 point)
Responses

A) The result is not a closed system.

B) The result is not a polynomial.

C) The result is a polynomial.

D) The result is unknown.

Answer 1

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.

1. **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).

2. **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.**