Question

question. 12
will a polynomial times a polynomial always equal a polynomial?
a. no, because polynomials are closed under multiplication.
b. no, because polynomials are not closed under multiplication.
c. yes, because polynomials are closed under multiplication.
d. yes, because polynomials are not closed under multiplication.
= 8x³ + 11x

Explanation:

To determine the answer, we recall the concept of closure under multiplication for polynomials. A set is closed under an operation if performing that operation on elements of the set always results in an element of the same set. Polynomials are closed under multiplication, meaning that multiplying two polynomials will always result in another polynomial.

• Option A is incorrect because stating "No" and then giving a reason that polynomials are closed under multiplication is contradictory (closure under multiplication means the result should be a polynomial, so the answer should be "Yes").
• Option B is incorrect because polynomials are closed under multiplication, so the "No" and the reason are both wrong.
• Option D is incorrect because the reasoning (polynomials not being closed under multiplication) contradicts the fact that they are closed, and the "Yes" with that reason is illogical.
• Option C is correct because it correctly states that the product of two polynomials is a polynomial, which is due to polynomials being closed under multiplication.

Answer:

C. Yes, because polynomials are closed under multiplication.