Question

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

a 4x3 + 12x2 + 28x may or may not be a polynomial
b 4x3 + 12x2 + 28x is a polynomial
c 4x4 + 12x3 + 28x2 may or may not be a polynomial
d 4x4 + 12x3 + 28x2 is a polynomial

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