Question

The area of a rectangle shown is ${\mathit{x}}^{\mathbf{3}}\mathbf{-}\mathbf{2}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{5}\mathit{x}$square units. What is the length?

Short answer

The length of rectangle is $x^2-2x+5$.

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:

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

Step 2. Write the factors and equate.

Now, factorizing the area of the polynomial:

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

Step 3. Write the conclusion.

Comparing the length and width x:

The length of the rectangle is $x^2-2x+5$.