The side of a square measures (4x − 7) 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)

Question

phillip399122 phillip399122

29-07-2017
Mathematics

contestada

The side of a square measures (4x − 7) 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)

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Part A. A square is a two-dimensional shape with 2 sets of equal, parallel sides. The area of a square is equal to the square of its side. So, if the side measures (4x-7) units, then the area would be (4x-7)^2.

Part B. Let's expand the binomial in part A first. That would be equal to 16x^2 - 56x +49. There are different classifications of equation. There are linear equations, quadratic equations and exponential equations. In this case, the equation is a quadratic equation because it possesses the standard formula of a quadratic equation which is equal to ax^2 + bx + c = 0. On the other hand, the degree of the equation is the highest power of the variable. Since the highest degree is 16x^2, then the degree is 2.

Part C. Closure Property of Multiplications is if a and b are real unique numbers, then their product is also a unique real number. Part A demonstrates this property in a way because 4x-7 is multiplied with itself. It is considered unique because you can have different values for x. They are still unique. Also, the expanded quadratic equation is also unique.