Question

The area of a rectangle is represented by the 1

expression (2x3 - x2 - 18x + 9). If the width is b
represented by the expression (x - 3), find the
expression representing the length.

Answer 1

The expression representing the length of the rectangle is obtained by dividing the area of the rectangle, (2x^3 - x^2 - 18x + 9), by the width, (x - 3), which gives us 2x^2 + 5x - 3.

Step-by-step explanation:

To find the expression representing the length of a rectangle, we divide the area of the rectangle by the width. The area is given as (2x3 - x2 - 18x + 9), and the width is given as (x - 3).

To find the length, we perform polynomial division:

1. Divide the first term of the area's expression (2x3) by the first term of the width's expression (x), resulting in 2x2.
2. Multiply the entire width (x - 3) by this result (2x2) and subtract it from the area's expression.
3. Repeat the process with the new polynomial obtained after subtraction until the remainder is zero or of lesser degree than the width's expression.

If done properly, you'll get the expression for the length. In this case, after performing the polynomial division:

(2x3 - x2 - 18x + 9) ÷ (x - 3) = 2x2 + 5x - 3

Therefore, the expression representing the length is 2x2 + 5x - 3.