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 a polynomial.
The result is a polynomial.

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

The result is unknown.

1 answer

To analyze the multiplication problem \((9x^3+76)(x−25)\), we can determine the nature of the result based on the expression itself.

  1. Identifying the Components:

    • The expression \(9x^3 + 76\) is a polynomial of degree 3 (since the highest exponent of \(x\) is 3).
    • The expression \(x - 25\) is a polynomial of degree 1.
  2. Polynomial Multiplication:

    • When we multiply two polynomials together, the resulting expression is also a polynomial. The degree of the resulting polynomial is the sum of the degrees of the two polynomials. In this case, the degree will be \(3 + 1 = 4\).
  3. Conclusion:

    • Therefore, the result of the multiplication \((9x^3+76)(x−25)\) will be a polynomial.

Given the options:

  • The correct response is: The result is a polynomial.