Question

Use the image to answer the question.

A rectangle has its length labeled x-squared minus x plus 1 and its width labeled 2 x-squared plus 3 x minus 2.

A poster board for a science project is in the shape of a rectangle. Determine the polynomial expression that represents the perimeter of the poster board.

(1 point)
Responses

6x2+4x−2
6 x squared plus 4 x minus 2

10x2+2x−2
10 x squared plus 2 x minus 2

6x2+8x+6
6 x squared plus 8 x plus 6

3x2+2x−1

Answer 1

To find the polynomial expression that represents the perimeter of the rectangle, we can use the formula for the perimeter \( P \) of a rectangle, which is:

\[
P = 2 \times (\text{length} + \text{width})
\]

Given that:
- Length \( L = x^2 - x + 1 \)
- Width \( W = 2x^2 + 3x - 2 \)

First, we need to calculate the sum of the length and width:

\[
L + W = (x^2 - x + 1) + (2x^2 + 3x - 2)
\]

Combine like terms:

\[
L + W = (x^2 + 2x^2) + (-x + 3x) + (1 - 2)
\]

\[
L + W = 3x^2 + 2x - 1
\]

Now, we will calculate the perimeter:

\[
P = 2 \times (L + W) = 2 \times (3x^2 + 2x - 1)
\]

Distributing the 2:

\[
P = 6x^2 + 4x - 2
\]

Therefore, the polynomial expression that represents the perimeter of the poster board is:

**6 x squared + 4 x - 2**

Thus, the answer is:

**6x² + 4x - 2**