To determine the nature of the result of the multiplication problem \((9x^3 + 76)(x - 25)\), let's analyze the components:
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\(9x^3 + 76\) is a polynomial. It has a term with \(x\) (specifically \(x^3\)), and a constant term (76), which makes it a polynomial of degree 3.
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\(x - 25\) is also a polynomial. It is a first-degree polynomial.
Now, when we multiply two polynomials, the result is always a polynomial. Specifically:
- The degree of the resulting polynomial will be the sum of the degrees of the two polynomials being multiplied. In this case, the degree of \(9x^3 + 76\) is 3 and the degree of \(x - 25\) is 1. Therefore, the degree of the product is \(3 + 1 = 4\).
Thus, the multiplication \((9x^3 + 76)(x - 25)\) will yield a polynomial of degree 4.
Given this reasoning, the correct statement is:
The result is a polynomial.
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