# For each statement, choose whether it is always, sometimes, or never true.

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## Question:

For each statement, choose whether it is always, sometimes, or never true. An integer multiplied by an integer is an integer.
An integer divided by an integer is an integer.
An integer subtracted from an integer is an integer.
A polynomial added to a polynomial is a polynomial.
A polynomial divided by a polynomial is a polynomial.
A polynomial subtracted from a polynomial is a polynomial.

An integer multiplied by an integer is an integer. (Always true)

Reason: The set of integers is closed under multiplication

An integer divided by an integer is an integer. (Sometimes true)

Reason: A set of integers is not closed under division. However, it is sometimes possible to get an integer as a result of the division of two integers. For example, 4/2  =  2

An integer subtracted from an integer is an integer. (Always true)

Reason: A set of integers is closed under subtraction

A polynomial added to a polynomial is a polynomial. (Always true)

Reason: Addition of two polynomials always gives another polynomial as a result of grouping similar elements together