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Q30.

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 ${x}^{2}-2x+5$.