What must be true about this multiplication problem?

(9x3+76)(x−25)


(1 point)
Responses

The result is not a closed system.
The result is not a closed system.

The result is unknown.
The result is unknown.

The result is not a polynomial.
The result is not a polynomial.

The result is a polynomial.

1 answer

To analyze the multiplication problem \((9x^3 + 76)(x - 25)\), we note that:

  1. Polynomial Definition: A polynomial is an expression that can consist of variables, coefficients, constants, and non-negative integer exponents. The expression \(9x^3 + 76\) is a polynomial, and \(x - 25\) is also a polynomial.

  2. Multiplication of Polynomials: The product of two polynomials is also a polynomial. Specifically, multiplying \(9x^3 + 76\) (which is a polynomial of degree 3) with \(x - 25\) (which is a polynomial of degree 1) will result in a polynomial of degree \(3 + 1 = 4\).

Therefore, we can conclude that the correct response regarding this multiplication problem is:

The result is a polynomial.