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? (3 points)

Given: Side of the Square = ( 3x - 6 ) units

Part A).

Area of the Square = Side × Side = ( 3x - 6 )( 3x - 6 ) = ( 3x - 6 )²

                                = ( 3x )² + 6² - 2 × 3x × 6

                                = 9x² + 36 - 36x

Part B).

Degree of a polynomial is the height power of the polynomial.

Degree of the 9x² + 36 - 36x is 2.

Since Polynomial representing Area of the square has 3 terms and degree = 2.

So the Polynomial is a Trinomial polynomial and Quadratic polynomial.

Part C).

Closure Property of polynomial is always under multiplication means when two polynomials are multiplies then the resulting product is also a polynomial.

Here, Also two linear polynomial are multiplied and we get a quadratic polynomial.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

answer: 5

step-by-step explanation: