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
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
