The area, in square feet, of a rectangular parking lot is represented by the expression x^3 + 27. Let x + 3 represent the length, in feet, of the parking lot. Which expression represents the width, in feet, of the parking lot?
x² - 3x + 9 represents the width of the parking lot.
To find the width of the rectangular parking lot given the area and length, we can factor the area expression (x^3 + 27) using the factored form of a sum of cubes, which results in ((x + 3)(x^2 - 3x + 9)).
This expression is derived from factoring the area (x^3 + 27) as a sum of cubes, giving the factors ((x + 3)(x^2 - 3x + 9)). Here, (x + 3) is the length, so the remaining factor, (x^2 - 3x + 9), correctly represents the width of the parking lot.
This expression does not represent the correct factorization of the area. The correct factorization of (x^3 + 27) does not yield this expression, which can be verified by trying to expand it back to the original cubic form. Therefore, it cannot represent the width of the parking lot.
While this expression is related to the length of the parking lot, it incorrectly suggests that the width is the square of the length. The width must be a distinct factor that, when multiplied by the length, results in the area (x^3 + 27). Thus, this option does not represent the width.
This expression could be mistakenly derived from a different factorization but does not relate to the area (x^3 + 27) when factored correctly. It does not fit the derived factors from the sum of cubes, hence it cannot be the width of the parking lot.
This choice represents the length of the parking lot, not the width. The width must be a separate expression that complements the length to form the area, which is not achieved by using the length itself.
The width of a rectangular parking lot can be determined by factoring the area expression (x^3 + 27) into ((x + 3)(x^2 - 3x + 9)). The correct expression for the width is (x^2 - 3x + 9), as it is the factor remaining after identifying the length as (x + 3). Understanding how to manipulate polynomial expressions is crucial in solving for dimensions in geometric contexts.
Related Questions
View allWhat is the greatest common factor of the three terms in the polynomia...
The tables above list some of the values of three functions, f, g, and...
If y < x < 0, which of the following numbers is greatest?
Under controlled conditions, the number of a certain type of bacteria...
Which of the following is one of the solutions of the equation x² - 2x...
Related Quizzes
View allAmerican Government CLEP Cheat Sheet
CLEP College Algebra Exam Questions
CLEP College Mathematics Exam Secrets Study Guide
CLEP History of the United States II Examination Guide
CLEP History of the United States II Examination Guide
Humanities CLEP Test Study Guide
CLEP Humanities Test Questions
CLEP Introductory Psychology Examination Guide
College Level Examination Program CLEP Exams Hack
CLEP Western Civilization I Exam Secrets Study Guide
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations