Understanding Closure Properties

What is the closure property concerned with?

• Whether a set can be divided by zero

• Whether a set contains only positive numbers

• Whether operations on elements of a set result in elements within the same set

• Whether a set is finite or infinite

Which operations are whole numbers closed under?

• Addition and subtraction

• Subtraction and division

• Addition and multiplication

• Multiplication and division

Why are whole numbers not closed under division?

• Division results in negative numbers

• Division always results in a whole number

• Division results in fractions or decimals

• Division by zero is undefined

Which operations are integers closed under?

• Subtraction, multiplication, and division

• Addition, subtraction, and multiplication

• Addition, subtraction, and division

• Addition, multiplication, and division

What happens when you add two polynomials?

• You get a polynomial

• You get a fraction

• You get a variable

• You get a constant

How are polynomials affected by subtraction?

• Subtraction results in a variable

• Subtraction results in a polynomial

• Subtraction results in a non-polynomial

• Subtraction results in a constant

What is the result of multiplying two polynomials?

• A polynomial

• A variable

• A fraction

• A constant

Why is division of polynomials not always closed?

• It always results in a polynomial

• It can result in a non-polynomial if the denominator contains a variable

• It results in a variable

• It results in a constant

What is a key issue with dividing polynomials?

• Variables in the denominator can lead to non-polynomials

• The numerator must be zero

• The denominator must be zero

• The result is always a polynomial

When dividing polynomials, what can sometimes happen?

• You always get a polynomial

• You never get a polynomial

• You sometimes get a polynomial

• You always get a constant