Question

the volume of a rectangular dog kennel is modeled by the polynomial x3 +14x2 +60+72. If the height of the kennel is modeled by (x+2) and the length and width are equal to each other, what expression could represent the dog kennel

Answer 1

Answer: I don’t really know

Answer 2

The expression could represent the dog kennel is (x + 2)(x + 6)²

What expression could represent the dog kennel

From the question, we have the following parameters that can be used in our computation:

Volume = x³ + 14x² + 60x + 72

Height = x + 2

Dividing the Volume by the Height , we have

x² + 12x+ 36

x + 2 | x³ + 14x² + 60x + 72

x³ + 2x²

--------------------------------------------------------

12x² + 60x + 72

12x² + 24x

--------------------------------------------------------

36x + 72

36x + 72

--------------------------------------------------------

0

So, we have

x³ + 14x² + 60x + 72 = (x + 2)(x² + 12x+ 36)

Expand

x³ + 14x² + 60x + 72 = (x + 2)(x + 6)²

Hence, the expression could represent the dog kennel is (x + 2)(x + 6)²