If this is the case, then you know by the polynomial remainder theorem that 
is a factor of 
, so there is some polynomial 
such that
So nobody is smart enough to answer my question?
2 answers:
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Answer:
Integers, whole numbers and polynomials are sets of closed under multiplication.
Only Irrational numbers are not the sets of closed under multiplication.
Step-by-step explanation:
To find : Which of the following sets are closed under multiplication?
1. Integers
Yes, integers is a sets of closed under multiplication as if you multiply an integer by an integer, you will always get another integer.
Example - is an integer
2. Irrational numbers
No, irrationals are not closed under multiplication.
Example - is a rational number
3. Whole numbers
Yes, whole numbers is a sets of closed under multiplication as if you multiply a whole number by a whole number, you will always get another whole number.
Example - is a whole number
4. Polynomials
Yes, polynomial is sets of closed under multiplication as if you multiply the variables' exponents are added, and the exponents in polynomials are whole numbers so the new exponents will be whole numbers.
Example - is a polynomial.
