Answer:

The dimensions of the base of the swimming pool is (x + 2) by (3x + 2).

Step-by-step explanation:

Rectangular volume is given to be : l × w × h

3x³ - 4x² - 28x - 16 = l × w × (x - 4)

3x³ - 4x² -28x - 16 = lw(x - 4)

Divide both sides by x - 4. We'll be left with,

3x² + 8x + 4

Factor 3x² + 8x + 4 to have our length and height.

3x² + 8x + 4 = (x + 2)(3x + 2)

Therefore, the dimensions of the base of the swimming pool is (x + 2) by (3x + 2).