The diagram at the right shows the basic dimensions for a window. The glass portion of the window has a height-to-width ratio of [b]3 : 2[/b]. The framework adds [b]6[/b] inches to the width and [b]10[/b] inches to the height.[br][br][b][u]a.[/u][/b] Write a polynomial expression that represents the total area of the window, including the framework.[br][br][b][u]b.[/u][/b] Find the area when [b]x[/b] = [b]10[/b], [b]11[/b], [b]12[/b], [b]13[/b] and [b]14[/b].

a) Verbal Model:[br][br]Total Area = Height of window [math]\cdot[/math] Width of window[br][br]Total Area = [b][i]A[/i][/b]       (square inches)[br][br]Height of window = [math]3x+10[/math]  (inches)[br][br]Width of window = [math]\left(2x+6\right)[/math]  (inches)[br][br]Algebraic Model:[br][br][math]A=\left(3x+10\right)\cdot\left(2x+6\right)[/math]     [color=#0000ff]Area model[/color][br][br] [math]=6x^2+18x+20x+60[/math]   [color=#0000ff]FOIL pattern[br][/color][br] [math]=6x^2+38x+60[/math]    [color=#0000ff]Combine like terms[/color]

You can evaluate the polynomial expression [math]6x^2+38x+60[/math] by substituting [b][i]x[/i][/b]-values. For instance, to find the total area of the window when [math]x=-10[/math], substitute [b][i]10[/i][/b] for [b][i]x[/i][/b].[br][br][math]A=6x^2+38x+60[/math][br][br] [math]=6\left(10\right)^2+38\left(10\right)+60[/math][br][br] [math]=600+380+60[/math][br][br] [math]=1040[/math][br][br]The areas for all five [b][i]x[/i][/b]-values are listed in the table.[br]