Question

The side of a square measures (3x − 6) units.

Part A: What is the expression that represents the area of the square? Show your work to receive full credit. (4 points)

Part B: What are the degree and classification of the expression obtained in Part A? (3 points)

Part C: How does Part A demonstrate the closure property for polynomials?

Answer 1

Step-by-step explanation:

The side of a square measures (3x − 6) units.

Answer 2

Step-by-step explanation:

Given that:

• The side of a square is (3x-6) units.

Note that: (a+b)² = a³+2ab+b²

Part A:-

The area of the square is

A = (3x-6)(3x-6)

= (3x)²+2(3x)(-6)+(-6)²

= 9x²-36x+36.

Part B:-

The area is a 2nd-degree polynomial,or a quadratic function,or parabola.

Part C:-

A 2nd-degree polynomial of the form,

f(x) = ax¹+bx¹+cx⁰ = ax²+bx+c

Where a,b,c are constant (coefficients of the polynomial).

a =9, b = -36, c = 36.

The polynomial is closure it is completely defined by multiply and addition operation.