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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)

Answer 1

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

\[ \text{Area} = \text{base} \times \text{height} \]

In this case, the base is given as \(x^2 + 2\) and the height is labeled as \(x - 1\).

Now, to find the area of the park, substitute the expressions for the base and height into the formula:

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

Now, we need to expand this expression:

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

Calculating each term:

1. \(x^2 \cdot x = x^3\)
2. \(x^2 \cdot (-1) = -x^2\)
3. \(2 \cdot x = 2x\)
4. \(2 \cdot (-1) = -2\)

Now, combine these results:

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

Thus, the polynomial expression that represents the area of the park is:

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