Answer:
The correct option is;
x³ + 4·x² + 3·x < x³ + 13·x² + 54·x + 72.
Step-by-step explanation:
The given parameters are;
The basic plan of the decorator = x wall-color options, x + 1 ceiling-colr options, and x + 3 floor options
The gold plan of the decorator = All of the basic plan options plus 3 additional options in each category
Therefore, the gold plan of the decorator = (x + 3) wall-color options, (x + 1 + 3) ceiling-color options, and (x + 3 + 3) floor options
The total number unique layouts offered by the basic plan = x × (x + 1) × (x + 3) = x³ + 4·x² + 3·x
Also, the total number unique layouts offered by the gold plan = (x + 3) × (x + 1 + 3) × (x + 3 + 3) = (x + 3) × (x + 4) × (x + 6) = x³ + 13·x² + 54·x + 72
Which gives;
The comparison between the total number of unique layouts offered by the basic and gold plans as x³ + 4·x² + 3·x < x³ + 13·x² + 54·x + 72.
