Question

question 23 of 24 step 1 of 2 an open - top box is to be constructed from a sheet of tin that measures 22 inches by 14 inches by cutting out squares from each corner as shown and then folding up the sides. let v(x) denote the volume of the resulting box. step 1 of 2: write v(x) as a product of linear factors.

Explanation:

Step1: Determine length, width, height

When we cut out a square of side \( x \) from each corner, the length of the box becomes \( 22 - 2x \) (subtracting \( x \) from both ends), the width becomes \( 14 - 2x \), and the height is \( x \).

Step2: Volume formula for box

The volume \( V(x) \) of a rectangular box is given by \( V=\text{length}\times\text{width}\times\text{height} \). Substituting the values we found, we get \( V(x)=x(22 - 2x)(14 - 2x) \).

Answer:

\( V(x)=x(22 - 2x)(14 - 2x) \)