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

Students were enquired to answer a question at education and to indicate what is most important for them to succeed. Of the many comments, the one which that stood out was practice. Successful persons commonly not born successful; they become successful by hard work and determination. This is how you can attain your goals. Below are one of the answer and question example that you possibly will work with to practice and enrich your practical knowledge and also give you insights that should guide you to preserve your study in school.

## 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

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A polynomial divided by a polynomial is a polynomial. (Sometimes true)

Reason: Division of two polynomials sometimes gives a polynomial as the result, but not all the time

A polynomial subtracted from a polynomial is a polynomial. (Always true)

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

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