Question: Polynomials and Factoring Closure properties of integers and polynomials For each…

Polynomials and Factoring Closure properties of integers and polynomials

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

• An integer added to 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 divided by a polynomial is a polynomial.
• A polynomial subtracted from a polynomial is a polynomial.
• A polynomial multiplied by a polynomial is a polynomial.

Solution

For each statement, choose whether it is always, sometimes, or never true: 1. An integer added to an integer is an integer. - Always true. The sum of two integers is always an integer. 2. An integer divided by an integer is an integer. - Sometimes true. An integer divided by another integer is an integer only if the division is exact, otherwise it can result in a fraction. 3. An integer subtracted from an integer is an integer. - Always true. The result of subtracting one integer from another is always an integer. 4. A polynomial divided by a polynomial is a polynomial. - Sometimes true. The result can be a polynomial if the division is exact; otherwise, it can result in a rational expression. 5. A polynomial subtracted from a polynomial is a polynomial. - Always true. The difference of two polynomials is always a polynomial. 6. A polynomial multiplied by a polynomial is a polynomial. - Always true. The product of two polynomials is always a polynomial.