SOLUTION: The volume of the box below is represented by (x2 + 5x + 6)(x + 5). Find the polynomial that represents the area of the bottom of the box. Note that the height of the box is x +

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The volume of the box below is represented by (x2 + 5x + 6)(x + 5). Find the polynomial that represents the area of the bottom of the box. Note that the height of the box is x +       Log On


   

Question 64779: The volume of the box below is represented by
(x2 + 5x + 6)(x + 5). Find the polynomial that represents the area of the bottom of the box. Note that the height of the box is x + 2. (Hint: V= Area x height)
I appologize for the picture of the box not copying to this template. I hope that the question is still understandable.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
We are told that the Volume (V) of the box is area x height.

And we are also told that the Volume (V) of the box is (x^2 + 5x + 6)(x + 5) and that the height is x+2

Now we want to find the polynomial that represents the area of the bottom of the box.

The quadratic (x^2+5x+6) can be readily factored and we get:
(x^2+5x+6)=(x+2)(x+3) but we can see that x+2 is the height of the box so we'll replace it with (h) for height

V=area(a) x height (h) = (h)(x+3)(x+5) so we have
a x h =(h)(x+3)(x+5) divide both sides by h and we get:
a=(x+3)(x+5) expanding we have x^2+8x+15
Thus, the area of the bottom of the box is represented by the polynomial:
x^2+8x+15
Hope this helps. Happy holidays.------ptaylor