Question

question 5 of 10
which property of polynomial multiplication says that the product of two
polynomials is always a polynomial?

a. commutative

b. addition property of equality

c. distributive

d. closure

Explanation:

To determine the correct property, we analyze each option:

• Option A (Commutative): This property states that the order of multiplication doesn't matter (e.g., \(ab = ba\)), but it doesn't relate to the product being a polynomial.
• Option B (Addition property of equality): This is about adding the same value to both sides of an equation, not polynomial multiplication.
• Option C (Distributive): This property is about how multiplication distributes over addition (e.g., \(a(b + c)=ab + ac\)), but it's not about the product being a polynomial.
• Option D (Closure): The closure property for a set under an operation means that when the operation is performed on two elements of the set, the result is also an element of the set. For polynomial multiplication, the closure property means the product of two polynomials is always a polynomial.

Answer:

D. Closure