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.

A)

This option is always true.

Since, the integer is closed under multiplication.

B)

This option is not always true. It is sometimes true.

Because:

when 4 is divided by 2 then we get:

4÷2=2 which is an integer

But

3÷5 is not an integer it is a rational number.

C)

An integer subtracted from an integer is an integer.

This option is always true.

Since, the set of integers is closed under subtraction.

D)

A polynomial added to a polynomial is a polynomial.

This option is always true.

Because the set of polynomials is closed under addition.

E)

A polynomial divided by a polynomial is a polynomial.

This option is not always true.It is sometimes true.

Since if we divide x³ by x then we get the result as:

x³÷x=x² which is a polynomial.

but when we divide x by x³ then we get the result as:

x÷x³=1/x² which is not a polynomial function.

It is a rational function.

F)

A polynomial subtracted from a polynomial is a polynomial.

This is always true.

Because the set of polynomial is closed under subtraction.

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