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The rectangular-shaped landing area of (x + 5x2 + 4x + 20) ft? is shaded. The dimensions of the landing area can be found by factoring. What are the length and width of the landing area? (Assume x > 3.) Dft (smaller value) (larger value)

The rectangular-shaped landing area of (x + 5x2 + 4x + 20) ft? is shaded. The dimensions of the landing area can be found by factoring. What are the length and width of the landing area? (Assume x > 3.) Dft (smaller value) (larger value)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Factoring Polynomials to Find Dimensions** The rectangular-shaped landing area of \((x^3 + 5x^2 + 4x + 20) \text{ ft}^2\) is shaded. The dimensions of the landing area can be found by factoring. **Question:** What are the length and width of the landing area? (Assume \(x > 3\)). **Answer Format:** Specify the dimensions labeled as smaller value and larger value in feet. - **(_________) ft** (smaller value) - **(_________) ft** (larger value) **Graph/Diagram Explanation:** There is an illustration of two rectangles, one above the other. The first rectangle is labeled "(smaller value)" and the second rectangle is labeled "(larger value)". Additionally, there are lines indicating the input fields to enter the dimensions of the rectangular-shaped landing area. **Steps for Solving:** 1. Identify the polynomial expression for the area: \((x^3 + 5x^2 + 4x + 20) \text{ ft}^2\). 2. Factor the polynomial to find the expressions for length and width. 3. Solve for the values assuming \(x > 3\). 4. Enter the smaller value in the first rectangle and the larger value in the second rectangle. This exercise involves polynomial factoring, algebraic manipulations, and ensuring the final dimensions satisfy the condition \(x > 3\).
Transcribed Image Text:**Factoring Polynomials to Find Dimensions** The rectangular-shaped landing area of \((x^3 + 5x^2 + 4x + 20) \text{ ft}^2\) is shaded. The dimensions of the landing area can be found by factoring. **Question:** What are the length and width of the landing area? (Assume \(x > 3\)). **Answer Format:** Specify the dimensions labeled as smaller value and larger value in feet. - **(_________) ft** (smaller value) - **(_________) ft** (larger value) **Graph/Diagram Explanation:** There is an illustration of two rectangles, one above the other. The first rectangle is labeled "(smaller value)" and the second rectangle is labeled "(larger value)". Additionally, there are lines indicating the input fields to enter the dimensions of the rectangular-shaped landing area. **Steps for Solving:** 1. Identify the polynomial expression for the area: \((x^3 + 5x^2 + 4x + 20) \text{ ft}^2\). 2. Factor the polynomial to find the expressions for length and width. 3. Solve for the values assuming \(x > 3\). 4. Enter the smaller value in the first rectangle and the larger value in the second rectangle. This exercise involves polynomial factoring, algebraic manipulations, and ensuring the final dimensions satisfy the condition \(x > 3\).
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