Which of the following responses shows that polynomials form a closed system under multiplication?

13)(x4−2)
left parenthesis Start Fraction 1 over 3 End Fraction right parenthesis left parenthesis Start Fraction x over 4 End Fraction minus 2 right parenthesis

5x⋅2
5 x times 2

2x3+x2
2 x cubed plus x squared

5⋅3
5 times 3
Remaining Attempts : 3

5 answers

The correct response that shows that polynomials form a closed system under multiplication is:

2x^3 + x^2
It was a
I apologize for the incorrect response.

The correct response that shows that polynomials form a closed system under multiplication is:

5x⋅2

This equation represents multiplying a polynomial (5x) by a constant (2), which still results in a polynomial.
What must be true about this multiplication problem?

(9x3+7/6)(x−2/5)
The result is not a polynomial.
The result is not a polynomial.

The result is unknown.
The result is unknown.

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

The result is a polynomial.
The correct answer is:

The result is a polynomial.

When multiplying two polynomials, the result will always be a polynomial.