SOLUTION: Solve the problem The volume of a box is {{{2p^4 + 17p^3 + 21p^2}}}. The height is p, and the width is p + 7. What is the length?

The volume of a box is . The height is p, and the width is p + 7. What is the length?


Volume = length x width x height

2p^4  + 17p^3  + 21p^2 = length x (p+7) x p

2p^4  + 17p^3  + 21p^2 = length x (p^2 + 7p)

length = 

length = 

             ___2p^3+_3p^2____________
      p+7 ) 2p^4  + 17p^3  + 21p^2
               2p^4  + 14p^3
              ________________
                              3p^3   + 21p^2
                              3p^3   + 21p^2
                              _______________
                                                  0

length =  = 2p^3 + 3p^2 = p^2(2p+3)

Hope that helps!