5. A Rectangular Field The trinomial (x + 9x + 18) square meters represents the area of a rectangular field. Find two binomials that might represent the length and width of the field.

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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### Problem 95: A Rectangular Field

The trinomial \(x^2 + 9x + 18\) square meters represents the area of a rectangular field. Find two binomials that might represent the length and width of the field.

**Solution Explanation:**
- To find the binomials representing the length and width, factor the trinomial.
- Look for two numbers that multiply to 18 (the constant term) and add to 9 (the coefficient of the linear term).
- In this case, the factors are \(3\) and \(6\).
- Therefore, the two binomials are \((x + 3)\) and \((x + 6)\).
- This means the area of the rectangle can be expressed as \((x + 3)(x + 6) = x^2 + 9x + 18\).

**Visual Representation:**
There are no graphs or diagrams to explain for this exercise.
Transcribed Image Text:### Problem 95: A Rectangular Field The trinomial \(x^2 + 9x + 18\) square meters represents the area of a rectangular field. Find two binomials that might represent the length and width of the field. **Solution Explanation:** - To find the binomials representing the length and width, factor the trinomial. - Look for two numbers that multiply to 18 (the constant term) and add to 9 (the coefficient of the linear term). - In this case, the factors are \(3\) and \(6\). - Therefore, the two binomials are \((x + 3)\) and \((x + 6)\). - This means the area of the rectangle can be expressed as \((x + 3)(x + 6) = x^2 + 9x + 18\). **Visual Representation:** There are no graphs or diagrams to explain for this exercise.
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