Abox with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. find the largest volume that such a box can have.

Step-by-step explanation:

With the information you have provided, the volume can only be stated as a third degree polynomial.  We do not know the measurements of the square cut out of each corner, we can only call it "x".

If each side of the square measures 3 feet wide and we cut out 2 squares from a side, the length of that side is 3 - 2x.  Volume is length times width times height.  The length and the width will both be 3 - 2x, and the height is the measurement of x.  But since we don't know it, the height is just x.  Multiplying the length times the width times the height looks like this:

(3 - 2x)(3 - 2x)(x)

When you FOIL all this together you get a third degree polynomial

If you know the measurement of the squares cut out, plug that value in for x and get the volume in a number.

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step-by-step explanation: