Question

M

IF THE VOLUME OF THE BOX BELOW IS
x3 + 6x2 + 9x + 4
AND THE WIDTH OF THE BOX IS x + 4,
THEN FIND THE LENGTH AND HEIGHT OF
THE BOX

Answer 1

The length of the box is (x + 1)

The height of the box is (x + 1)

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).