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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