\begin{tabular}{l|c|}\( \begin{array}{l}\text { 25a) Gary is building a square table for a kitchen. In his } \\ \text { initial sketch, each side measured } x \text { feet. After rearranging } \\ \text { some furniture, he realized he would have to add one foot }\end{array} \) & \( \begin{array}{c}25 \\ \text { of } \\ \text { to the length and remove one foot from the width and } \\ \text { have a rectangular table instead. Write a polynomial to }\end{array} \) \\ \hline represent the area of the rectangular table. \end{tabular}

To find the area of the rectangular table after Gary's adjustments, we start with the initial area of the square table, which is \(x^2\). Given that he adds one foot to the length and removes one foot from the width, the new dimensions would be \(x + 1\) (length) and \(x - 1\) (width). The area \(A\) of the rectangular table can be expressed as: \[ A = (x + 1)(x - 1) \] Using the Difference of Squares formula, this simplifies to: \[ A = x^2 - 1 \] Now, Gary has a polynomial representing the area of his new rectangular table! --- Did you know that tables have been a fixture in human homes for centuries? The design and shape of tables have evolved significantly since ancient times, from simple hearths in caves to the elaborately crafted tables of medieval banquets. Whether round, square, or rectangular, tables are at the center of dining, meetings, and social gatherings, making them an essential part of our everyday lives. For a real-world application, let’s say you want to recreate Gary’s project but with a twist. Imagine hosting a dinner party! You can use the dimensions \(x + 1\) and \(x - 1\) to ensure everyone has ample room or even adjust them further to create a custom space for food, drinks, and decoration. With careful planning and the polynomial you derived, you can ensure that your table fits perfectly in your dining area!