How to Write and Simplify a Polynomial for Area

TL;DR

To write and simplify a polynomial for the window area, first define the height as 3x and width as 2x. Include the trim, adding 8 inches to height and 7 inches to width. The resulting polynomial for the total area is 6x² + 37x + 56.

Transcript

We're told that the glass portion of the window shown below-- that's the window-- has a height to width the ratio of 3:2. So the height of the glass portion can be represented as 3x and the width of the glass portion can be represented as 2x. The wood trim adds 7 inches to the total width and 8 inches to the total height. So let me write that down.... Read More

Key Insights

• 🥳 The glass portion of the window has a height-to-width ratio of 3:2.
• 🤌 The wood trim increases the total height by 8 inches and the total width by 7 inches.
• 🪟 The total area of the window is determined by multiplying the height and width.

Questions & Answers

Q: How is the height of the glass portion determined?

The height of the glass portion is represented by 3x, which is derived from the given ratio of 3:2.

Q: What is the impact of the wood trim on the height and width of the window?

The wood trim adds 8 inches to the total height and 7 inches to the total width of the window.

Q: How is the total area of the window calculated?

The total area is determined by multiplying the height (3x + 8) by the width (2x + 7).

Q: How can the polynomial expression (6x^2 + 37x + 56) be simplified?

The expression can be simplified by multiplying the terms using the distributive property and combining like terms, resulting in a simplified polynomial expression.

Summary & Key Takeaways

• The glass portion of the window has a height to width ratio of 3:2, with the height represented as 3x and the width as 2x.

• The wood trim adds 7 inches to the total width and 8 inches to the total height.

• The polynomial expression for the total area of the window, including the glass and wood, is (6x^2 + 37x + 56).