Question

question 10 of 10
which property of polynomial subtraction says that the difference of two
polynomials is always a polynomial?

a. distributive

b. multiplication property of equality

c. closure

d. commutative

Explanation:

To determine the correct property, we analyze each option:

• Option A (Distributive): Deals with distributing a factor over a sum/difference (e.g., \(a(b + c)=ab + ac\)), not about the result of subtraction being a polynomial. Eliminate A.
• Option B (Multiplication property of equality): Relates to multiplying both sides of an equation by a number, irrelevant to polynomial subtraction results. Eliminate B.
• Option C (Closure): A set is closed under an operation if applying the operation to two elements of the set gives another element of the set. Polynomials under subtraction: subtracting two polynomials gives a polynomial, so this is closure.
• Option D (Commutative): Deals with the order of operation (e.g., \(a + b = b + a\)), not about the result being a polynomial. Eliminate D.

Answer:

C. Closure