Question

Write the polynomial function that models the given situation.A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.

Answer 1

Answer:

$V(x)=(11-2x)(12-2x)x= 4 x^3- 46 x^2 + 132 x.$

Step-by-step explanation:

Consider the picture attached, which illustrates the process of making the box.

Observe that in figure (2) the sides of the rectangle were both reducing two times the length of the side of the square. Therefore, the sides of the new figure are 12-2x units and 11-2x units, respectively.

In figure (3), when the box is done, we see that its dimensions are 11-2x, 12-2x and x (width, length and high, respectively). Thus, by the formula of the volume of a box, we know that the volume V(x) is given by $V(x)= width\times length\times high=(11-2x)(12-2x)x.$ Solving the parenthesis, we get that $V(x)=4 x^3- 46 x^2 + 132 x.$