algebra 2 high school

Question

A 10 inch by 16 inch piece of cardboard is made into an open box by cutting our squares of side length x from each corner and folding up the sides. Find a polynomial in standard form for the volume of the box.

Answer 1

length of open box = 16 - 2x

 

Width of open box = 10 - 2x 

 

Height of open box = x

 

Volume of open box = L * W * H = (16 - 2X)(10 - 2X)X

 

 = 4X³ - 52X² + 160X  =   4X(X² - 13X + 40)   =   4X(X - 8)(X - 5)