SOLUTION: Geometry. The volume of the box is represented by(x^2 + 5x + 6)(x + 5). Find the polynomial that represents the area of the bottom of the box. One side has x+2 next to it.

Question 77887: Geometry. The volume of the box is represented by(x^2 + 5x + 6)(x + 5). Find the polynomial that represents the area of the bottom of the box.
One side has x+2 next to it.

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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

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