Question

what is an expression that can represent the area of the rectangular room? how can the expression be written in polynomial in standard form?show your work

Answer 1

The formula for determining the area of a rectangle is expressed as

Area = length * width

From the diagram,

Length = 3x + 6

Width = 4x - 1

The expression for the area of the room would be

$\begin{gathered} (3x\text{ + 6)(4x - 1) = (3x }\times\text{ 4x) + (3x }\times-\text{ 1) + (6 }\times4x)\text{ + (6}\times-1) \\ \text{Area = 12x}^2\text{ - 3x + 24x - 6} \\ \text{Area = 12x}^2\text{ + 21x - 6} \end{gathered}$

In standard polynomial form, the terms are arranged in decreasing order of exponents. Therefore, the expression in standard form is

$12x^2\text{ + 21x - 6}$