DESIGN. For Exercises 36-38, use the following information....

DESIGN. For Exercises $36-38,$ use the following information. Jill is designing a picture frame for an art project. She plans to have a square piece of glass in the center and surround it with a decorated ceramic frame, which will also be a square. The dimensions of the glass and frame are shown in the diagram at the right. jill determines that she needs 27 square inches of material for the frame. Write a polynomial equation that models the area of the frame.

DESIGN. For Exercises $36-38,$ use the following information. Jill is designing a picture frame for an art project. She plans to have a square piece of glass in the center and surround it with a decorated ceramic frame, which will also be a square. The dimensions of the glass and frame are shown in the diagram at the right. jill determines that she needs 27 square inches of material for the frame.
Write a polynomial equation that models the area of the frame.

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Key Concepts

Polynomial Modeling

This concept involves representing real-world scenarios using polynomial expressions. In this context, it refers to using algebraic expressions to model the area of the frame by setting up an equation that relates the dimensions of the inner and outer squares to the material used.

Geometric Area Calculation

Understanding how to calculate the area of geometric shapes, such as squares, is fundamental. The problem relies on calculating the area of both the inner square (the glass) and the outer square (the entire frame including the glass) to determine the area occupied solely by the frame.

Difference of Areas

This concept focuses on finding the area of the frame by subtracting the area of the inner square from the outer square. It involves creating an expression that captures this difference, which is key to setting up the correct polynomial equation for the scenario.

Translating Word Problems into Algebraic Equations

This involves reading a real-world problem carefully and converting the given information and relationships into an algebraic equation. In the context of this problem, the designer's requirement for a specific frame area leads to the formation of a polynomial equation that models the situation.

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