Respuesta :
The resultant polynomial which is the correct simplification and demonstration of the closure property of give expression is,
[tex]-5x^3 +4x^2- 5x[/tex]
This resultant expression is polynomial.
What is polynomial?
Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).
The given expression in the problem is,
[tex](3x^3 +2x^2 - 5x) - (8x^3 - 2x^2).[/tex]
Let the resultant polynomial of the above expression is f(x). Therefore,
[tex]f(x)=(3x^3 +2x^2 - 5x) - (8x^3 - 2x^2).[/tex]
To solve the above polynomial, open the bracket by multiplying the sign with inside values as,
[tex]3x^3 +2x^2 - 5x - 8x^3 +2x^2[/tex]
Separate the same power terms of the variables as,
[tex]f(x)=3x^3- 8x^3 +2x^2 +2x^2- 5x\\f(x)=-5x^3 +4x^2- 5x[/tex]
The resultant polynomial which is the correct simplification and demonstration of the closure property of give expression is,
[tex]-5x^3 +4x^2- 5x[/tex]
This resultant expression is polynomial.
Learn more about polynomial here;
https://brainly.com/question/24380382
