Final answer:
The area of the rectangle with height 3 and width 2x^2 + 3x - 5 is calculated as A = 6x^2 + 9x - 15, which represents the area as a function of x.
Step-by-step explanation:
The area of a rectangle is found by multiplying its height by its width. Given that the height is 3 and the width is expressed as the quadratic 2x^2 + 3x - 5, the area of the rectangle is obtained by multiplying 3 by the width expression. Therefore, the area A is:
A = height × width
A = 3 × (2x^2 + 3x - 5)
To express the area as a single polynomial, distribute the 3 across the terms in the parenthesis:
A = (3 × 2x^2) + (3 × 3x) - (3 × 5)
A = 6x^2 + 9x - 15
This polynomial represents the area of the rectangle as a function of x.