Question

Question 1(Multiple Choice Worth 1 points)

(06.04 MC)

Which statement shows how the product of (x + 3)2 demonstrates the closure property of multiplication?

x2 + 9 may or may not be a polynomial

x2 + 6x + 9 may or may not be a polynomial

x2 + 9 is a polynomial

x2 + 6x + 9 is a polynomial

Question 2 Multiple Choice Worth 1 points)

Answer 1

x² + 6x + 9 is a polynomial.

Explanation:

(x + 3)² is the same as the product (x + 3)(x + 3). Opening the bracket, we have

(x + 3)(x + 3) = x(x + 3) + 3(x + 3)

= x² + 3x + 3x + 9

= x² + 6x + 9

This implies that (x + 3)² is the same as x² + 6x + 9, and so, every value that satisfies x² + 6x + 9 will certainly satisfy (x + 3)².

Hence, the closure property.