Question

geometry the area of the base of a rectangular box measures (2x^2 + 4x - 3) square units. the height of the box measures (x) units. find a polynomial expression for the volume of the box.

Explanation:

Step1: Recall the volume formula for a rectangular box

The volume \( V \) of a rectangular box is given by the product of the area of the base \( B \) and the height \( h \), i.e., \( V = B\times h \).

Step2: Substitute the given expressions into the formula

We know that the area of the base \( B = 2x^{2}+4x - 3 \) and the height \( h=x \). So we multiply the area of the base by the height:
\[

$$\begin{align*} V&=(2x^{2}+4x - 3)\times x\\ &=2x^{2}\times x+4x\times x-3\times x\\ &= 2x^{3}+4x^{2}-3x \end{align*}$$

\]

Answer:

The polynomial expression for the volume of the box is \( 2x^{3}+4x^{2}-3x \) cubic units.