Question

you make a tin box by cutting x - inch - by - x - inch pieces of tin off of the corners of a rectangle and folding up each side. the plan for your box is shown.
a. what are the dimensions of the original piece of tin?
b. write a function that represents the volume v of the box. without multiplying, determine its degree.
the degree of the function is

Explanation:

Step1: Determine original dimensions

The length of the original tin is obtained by adding the two cut - off parts ($x$) to the length of the box after folding. So the length of the original tin is $(12 + 2x)$ inches, and the width is $(6 + 2x)$ inches. The dimensions of the original piece of tin are $(12 + 2x)$ by $(6+2x)$ inches.

Step2: Find volume function

The volume $V$ of a rectangular - box is given by $V=l\times w\times h$. After folding, the length $l = 12-2x$, the width $w = 6 - 2x$, and the height $h=x$. So the volume function is $V(x)=(12 - 2x)(6 - 2x)x$.

Step3: Determine the degree of the function

The degree of a polynomial is the highest power of the variable. Expand the factors: $(12 - 2x)(6 - 2x)x=(72-24x - 12x + 4x^{2})x=(72-36x + 4x^{2})x=72x-36x^{2}+4x^{3}$. The highest power of $x$ is 3, so the degree of the function $V(x)$ is 3.

Answer:

a. $(12 + 2x)$ by $(6 + 2x)$ inches
b. $V(x)=(12 - 2x)(6 - 2x)x$, degree is 3