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Expert-verified Found in: Page 514 ### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801 # The area of a rectangle shown is ${\mathbit{x}}^{\mathbf{3}}\mathbf{-}\mathbf{2}{\mathbit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{5}\mathbit{x}$ square units. What is the length? The length of rectangle is ${x}^{2}-2x+5$.

See the step by step solution

## Step 1. State the concept for area of rectangle.

The area of the rectangle is multiplication of the length and width.

The area of the rectangle is evaluated as:

$\begin{array}{c}\text{Area}=\text{length}×\text{width}\\ {x}^{3}-2{x}^{2}+5x=\text{length}×x\end{array}$

## Step 2. Write the factors and equate.

Now, factorizing the area of the polynomial:

$\begin{array}{c}\text{Area}={x}^{3}-2{x}^{2}+5x\\ =x\left({x}^{2}-2x+5\right)\\ \text{length}×\text{width}=\left({x}^{2}-2x+5\right).x\end{array}$

## Step 3. Write the conclusion.

Comparing the length and width x:

The length of the rectangle is ${x}^{2}-2x+5$. ### Want to see more solutions like these? 