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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![### Understanding Area of a Rectangle with Algebraic Expressions
In the given image, we have a rectangle. One side of the rectangle is labeled "x + 1," while the other side's length is marked with a question mark (?). The area of this rectangle is given as an algebraic expression:
\[
\text{Area} = x^2 + 6x + 5
\]
To find the missing dimension (?), you can use the formula for the area of a rectangle:
\[
\text{Area} = \text{length} \times \text{width}
\]
Here, one of the dimensions is \(x + 1\) and the area is \(x^2 + 6x + 5\). To find the missing dimension, you would set up the equation:
\[
(x + 1) \times (?) = x^2 + 6x + 5
\]
Solving this equation involves dividing the expression \(x^2 + 6x + 5\) by \(x + 1\).
### Factoring the Quadratic Expression
The expression \(x^2 + 6x + 5\) can be factored to find the missing dimension:
\[
x^2 + 6x + 5 = (x+1)(x+5)
\]
From this factorization, you can see the missing side is \(x + 5\).
### Conclusion
Therefore, the missing dimension of the rectangle is:
\[
x + 5
\]
This exercise demonstrates how to use algebraic expressions and factoring to determine unknown dimensions in geometric figures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F665c97df-0a92-4581-ae2a-55edc7588366%2Fd24c6ec6-ef24-420b-ba00-5612ed1953df%2Fvtjm4o5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Area of a Rectangle with Algebraic Expressions
In the given image, we have a rectangle. One side of the rectangle is labeled "x + 1," while the other side's length is marked with a question mark (?). The area of this rectangle is given as an algebraic expression:
\[
\text{Area} = x^2 + 6x + 5
\]
To find the missing dimension (?), you can use the formula for the area of a rectangle:
\[
\text{Area} = \text{length} \times \text{width}
\]
Here, one of the dimensions is \(x + 1\) and the area is \(x^2 + 6x + 5\). To find the missing dimension, you would set up the equation:
\[
(x + 1) \times (?) = x^2 + 6x + 5
\]
Solving this equation involves dividing the expression \(x^2 + 6x + 5\) by \(x + 1\).
### Factoring the Quadratic Expression
The expression \(x^2 + 6x + 5\) can be factored to find the missing dimension:
\[
x^2 + 6x + 5 = (x+1)(x+5)
\]
From this factorization, you can see the missing side is \(x + 5\).
### Conclusion
Therefore, the missing dimension of the rectangle is:
\[
x + 5
\]
This exercise demonstrates how to use algebraic expressions and factoring to determine unknown dimensions in geometric figures.
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