Answer:
(See explanation for further details)
Step-by-step explanation:
a) Let consider the polynomial  . The polynomial is in standards when has the form
. The polynomial is in standards when has the form  , where
, where  is the order of the polynomial. The example has the following information:
 is the order of the polynomial. The example has the following information:
 ,
,  ,
,  ,
,  ,
,  .
.
b) The closure property means that polynomials must be closed with respect to addition and multiplication, which is demonstrated hereafter:
Closure with respect to addition:
Let consider polynomials  and
 and  such that:
 such that:
 and
 and  , where
, where 

Hence, polynomials are closed with respect to addition.
Closure with respect to multiplication:
Let be  a polynomial such that:
 a polynomial such that:

And  an scalar. If the polynomial is multiplied by the scalar number, then:
 an scalar. If the polynomial is multiplied by the scalar number, then:

Lastly, the following expression is constructed by distributive property:

Hence, polynomials are closed with respect to multiplication.