Question

The side of a square measures (2x − 5) 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)

Answer 1

A. The area of a square is given as:

A = s^2

Where s is a measure of a side of a square. s = (2 x – 5) therefore,

A = (2 x – 5)^2                  

Expanding,

A = 4 x^2 – 20 x + 25

 

B. The degree of a polynomial is the highest exponent of the variable x, in this case 2. Therefore the expression obtained in part A is of 2nd degree.

Furthermore, polynomials are classified according to the number of terms in the expression. There are 3 terms in the expression therefore it is classified as a trinomial.

 

C. The closure property demonstrates that during multiplication or division, the coefficients and power of the variables are affected while during multiplication or division, only the coefficients are affected while the power remain the same.