SOLUTION: A box without a top is made from a rectangular piece of cardboard, with dimensions 6 ft by 8 ft, by cutting out square corners with side length x. Which equation can be used to

Question 1081905: A box without a top is made from a rectangular piece of cardboard, with dimensions 6 ft by 8 ft, by cutting out square corners with side length x.
Which equation can be used to determine the greatest possible volume of the cardboard box?
(6−x)(8−x)x=0
(8−6x)(6−8x)=0
(8x−6)(6x−8)=0
(8−2x)(6−2x)x=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If 8 is the old length, then 8-2x is the new length because we take x from both sides (there are 2 corner edges being cut off) to shrink down the length.

Similarly, 6 is the old width and 6-2x is the new width.

x is the height

Volume = (length)*(width)*(height)
Volume = (8-2x)*(6-2x)*(x)

The closest choice is choice D which is the answer. However, you aren't looking for the roots of this polynomial. Instead you're looking for the local max. So you shouldn't set the expression (8-2x)*(6-2x)*(x) equal to 0.
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