The complete statements are:
- Add [tex]\mathbf{3x^4 -7x^3 + 12x - 9}[/tex] to [tex]\mathbf{(2x)^3 +2.1x^2-11}[/tex].
- The sum is closed because the exponents are whole numbers,
- And by definition, the sum is a polynomial
The polynomial is given as:
[tex]\mathbf{3x^4 -7x^3 + 12x - 9}[/tex]
Polynomials are closed under addition.
This means that, when the polynomial is added to another, the exponents do not change.
The above highlight mean that:
[tex]\mathbf{3x^4 -7x^3 + 12x - 9}[/tex] cannot be added to [tex]\mathbf{5x^2 -(2x)^3 + (4x)^{-1}}[/tex] and [tex]\mathbf{-8x^{-2} +(3x)^3 -12x^6+ 7}[/tex], because they are not polynomials, and they have negative exponents
However, [tex]\mathbf{3x^4 -7x^3 + 12x - 9}[/tex] can be added to [tex]\mathbf{(2x)^3 +2.1x^2-11}[/tex]
The sum will give:
[tex]\mathbf{3x^4 -7x^3 + 12x - 9 + (2x)^3 +2.1x^2-11 = 3x^4 + x^3+2.1x^2 + 12x - 20}[/tex]
Read more about closure of polynomials at:
https://brainly.com/question/11391029
