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Answer:
The length of the box is (x + 1)
The height of the box is (x + 1)
Step-by-step explanation:
The given function representing the volume of the box is presented as follows;
V = x³ + 6·x² + 9·x + 4
The function representing the width of the box, W = x + 4
Therefore, we have;
(x³ + 6·x² + 9·x + 4)/(x + 4) = x² + 2·x + 1
x³ + 4·x²
2·x² + 9·x + 4
2·x² + 8·x
x + 4
Therefore, we have;
(x³ + 6·x² + 9·x + 4) = (x + 4) × (x² + 2·x + 1) = (x + 4) × (x + 1) × (x + 1)
(x³ + 6·x² + 9·x + 4) = (x + 4) × (x + 1) × (x + 1)
The width of the box = (x + 4)
The length of the box = (x + 1)
The height of the box = (x + 1).