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Question

A parallelogram has its length labeled x-squared plus 2 and its width labeled x plus 1. It has a dashed line for its height labeled x minus 1.

A park is in the shape of a parallelogram with dimensions shown. Determine the polynomial expression that represents the area of the park, in square units.

(1 point)
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Answer 1

To find the area of a parallelogram, you can use the formula:

\[ \text{Area} = \text{Base} \times \text{Height} \]

From the information provided:

• The base (length) is \( x^2 + 2 \)
• The height is \( x - 1 \)

Now we can substitute these expressions into the area formula:

\[ \text{Area} = (x^2 + 2)(x - 1) \]

Next, we need to expand this expression:

\[ \text{Area} = x^2 \cdot (x - 1) + 2 \cdot (x - 1) \]

Calculating each part:

1. \( x^2 \cdot (x - 1) = x^3 - x^2 \)
2. \( 2 \cdot (x - 1) = 2x - 2 \)

Now combine these results:

\[ \text{Area} = x^3 - x^2 + 2x - 2 \]

Putting it all together, the polynomial expression that represents the area of the park is:

\[ \boxed{x^3 - x^2 + 2x - 2} \]