Use the figure shown to the right to answer the questions below. Express each polynomial in standard form, that is, in descending powers of x. x+5 x+2 x+7 x+3 a. Write a polynomial that represents the area of the large rectangle.
Use the figure shown to the right to answer the questions below. Express each polynomial in standard form, that is, in descending powers of x. x+5 x+2 x+7 x+3 a. Write a polynomial that represents the area of the large rectangle.
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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Question
![**Using the Figure to Write a Polynomial**
In the provided exercise, you're tasked with using a diagram to find a polynomial expression for the area of a large rectangle.
**Diagram Explanation:**
The diagram consists of two rectangles:
1. **Large Rectangle:**
- **Length:** \(x + 7\)
- **Width:** \(x + 5\)
2. **Smaller Inner Rectangle:**
- **Length:** \(x + 3\)
- **Width:** \(x + 2\)
The outer rectangle encapsulates the inner rectangle with additional shaded space around it.
**Question:**
a. Write a polynomial that represents the area of the large rectangle.
**Solution Approach:**
To find the area of the large rectangle, multiply its length and width:
\[ \text{Area} = (x + 7)(x + 5) \]
Expand this expression to get the polynomial in standard form:
\[
(x + 7)(x + 5) = x^2 + 5x + 7x + 35 = x^2 + 12x + 35
\]
Thus, the polynomial representing the area is \(x^2 + 12x + 35\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6dc9660-7620-4f4d-948a-9c83904c3782%2F9c8787fc-3995-4b11-b5a2-561ade3d4cbe%2Fil8umx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using the Figure to Write a Polynomial**
In the provided exercise, you're tasked with using a diagram to find a polynomial expression for the area of a large rectangle.
**Diagram Explanation:**
The diagram consists of two rectangles:
1. **Large Rectangle:**
- **Length:** \(x + 7\)
- **Width:** \(x + 5\)
2. **Smaller Inner Rectangle:**
- **Length:** \(x + 3\)
- **Width:** \(x + 2\)
The outer rectangle encapsulates the inner rectangle with additional shaded space around it.
**Question:**
a. Write a polynomial that represents the area of the large rectangle.
**Solution Approach:**
To find the area of the large rectangle, multiply its length and width:
\[ \text{Area} = (x + 7)(x + 5) \]
Expand this expression to get the polynomial in standard form:
\[
(x + 7)(x + 5) = x^2 + 5x + 7x + 35 = x^2 + 12x + 35
\]
Thus, the polynomial representing the area is \(x^2 + 12x + 35\).
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