A rectangular area model has a width of 3x and a length of 2.1x - 4.3x - 6.1. Jordan determined the area of the rectangle by finding the product of (3x) (2.1x^2 - 4.3x - 6.1).

Complete the statement.
The area of the rectangle is ___.

1 answer

To find the area of the rectangle, we can multiply the width by the length. The width is given as \( 3x \) and the length is given as \( 2.1x^2 - 4.3x - 6.1 \).

Thus, the area \( A \) can be expressed as:

\[ A = \text{width} \times \text{length} = 3x \times (2.1x^2 - 4.3x - 6.1) \]

Now, to calculate the area:

  1. Distribute \( 3x \) across the polynomial:

\[ A = 3x \cdot 2.1x^2 + 3x \cdot (-4.3x) + 3x \cdot (-6.1) \]

  1. Perform the multiplication:

\[ A = 6.3x^3 - 12.9x^2 - 18.3x \]

So, the area of the rectangle is:

\[ \boxed{6.3x^3 - 12.9x^2 - 18.3x} \]