Question 77887
Volume(V) of a box equals Length(L) times Width(W) times Height(H) or:

V=LWH

Area(A) of the bottom of the box equals Length(L) times Width(W) or:

A=LW

Now we are told that:

V=(x^2+5x+6)(x+5)

Note that x^2+5x+6 is a quadratic equation in standard form:
A=1
B=5
C=6

If the A coefficient of a quadratic is 1 and if the quadratic is factorable, then the B coefficient will always be the sum of the factors of the C coefficient.  What are the factors of the C coefficient?

6 times 1---No------------------doesn't add up to 5
-6 times -1--No-----------------doesn't add up to 5
3 times 2----Yes!------------------Bingo!

Now we have:

V=(x+3)(x+2)(x+5)

Now if a side has an (x+2) beside it, then I assume that this must be the height, so:
It this is not a correct assumption, then figure out which is the height and the length and width will be the other two terms.

A=LW=(x+3)(x+5) multiplying this out, we get

A=x^2+8x+15-----------------------ans


Hope this helps---ptaylor