By definition we have to:
A set has under an operation if performance of that operation on set members always produces a member of the same set; in this case we also say that the set is closed under the operation.
For this case we have the following polynomials:
[tex]4x ^ 2
x ^ 2 + 3x + 7[/tex]
Multiplying we have:
[tex](4x ^ 2) (x ^ 2 + 3x + 7) = 4x ^ 4 + 12x ^ 3 + 28x ^ 2
[/tex]
The product of two polynomials is also a polynomial.
Answer:
d [tex]4x ^ 4 + 12x ^ 3 + 28x ^ 2[/tex] is a polynomial
