Q30. - Algebra 1

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?

Step-by-Step Solution

Answer

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

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 $x^2-2x+5$.