SOLUTION: 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. I don't understand word problems, so if someone c

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Geometry -> SOLUTION: 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. I don't understand word problems, so if someone c      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 83590: 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.
I don't understand word problems, so if someone could please explain step by step that would be great. Thanx
Answer by jim_thompson5910(14933) About Me  (Show Source):
You can put this solution on YOUR website!
Since the formula for volume is

V=Area_of_base%2Aheight which is identical to V=length%2Awidth%2Aheight

If the height is x%2B5 (I don't see a height posted anywhere, double check the problem) then the area of the base is

x%5E2%2B5x%2B6

However, if thats not the case, then we must factor x%5E2%2B5x%2B6 into %28x%2B3%29%28x%2B2%29 to get

%28x%2B3%29%28x%2B2%29%28x%2B5%29

If the height is %28x%2B2%29 then the area is %28x%2B3%29%28x%2B5%29=x%5E2%2B8x%2B15


If the height is %28x%2B3%29 then the area is %28x%2B2%29%28x%2B5%29=x%5E2%2B7x%2B10