Question

Which statement shows how two polynomials 4x2 and x2 + 3x + 7 demonstrate the closure property when multiplied?

Answer 1

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:
 $4x ^ 2 x ^ 2 + 3x + 7$
 Multiplying we have:
 $(4x ^ 2) (x ^ 2 + 3x + 7) = 4x ^ 4 + 12x ^ 3 + 28x ^ 2$
 The product of two polynomials is also a polynomial.
 Answer:
 d $4x ^ 4 + 12x ^ 3 + 28x ^ 2$ is a polynomial