1.)
[tex]6x(3x^2 + 14x +8) \\ \\ \boxed{6x(3x+2)(x+4)}
[/tex]
2.)
[tex]100x^2-80x+16=(10x-4)^2[/tex]
Each side of the parking lot measure [tex]\boxed{10x-4 meters}[/tex]
3.)
[tex]\frac{3x^2+2x-1}{3x-1} \\ \\
\frac{(3x-1)(x+1)}{3x-1} \\ \\
\boxed{x+1}[/tex]
4.)
[tex]x^2 + (x+10)^2 = 50^2 \\ x^2 + x^2 + 20x +100 = 2,500 \\ 2x^2 + 20x - 2,400 = 0 \\ x^2 + 10x -1,200 = 0 \\ (x+40)(x-30)=0 \\ x=-40 ; \boxed{x=30}[/tex]
The two legs measure 30 and 40.
5.)
[tex]x^2 + (x+2)^2 = 34 \\ x^2 + x^2 +4x+4=34 \\ 2x^2+4x-30=0 \\ x^2+2x-15=0 \\ (x+5)(x-3)=0 \\ x=-5 ; \boxed{x=3}[/tex]
The tabletops measure 3ftx3ft and 5ftx5ft.
