Questions: Write a polynomial that represents the area of the following rectangle.

Write a polynomial that represents the area of the following rectangle.
Transcript text: Write a polynomial that represents the area of the following rectangle.
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Solution

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Solution Steps

Step 1: Identify the dimensions of the rectangle

The given dimensions of the rectangle are:

  • Length: \(5x - 8\)
  • Width: \(3x + 4\)
Step 2: Write the formula for the area of a rectangle

The area \(A\) of a rectangle is given by the formula: \[ A = \text{Length} \times \text{Width} \]

Step 3: Substitute the given dimensions into the area formula

Substitute the given expressions for length and width into the formula: \[ A = (5x - 8) \times (3x + 4) \]

Step 4: Expand the polynomial

Use the distributive property (FOIL method) to expand the product: \[ A = (5x - 8)(3x + 4) \] \[ A = 5x \cdot 3x + 5x \cdot 4 - 8 \cdot 3x - 8 \cdot 4 \] \[ A = 15x^2 + 20x - 24x - 32 \]

Step 5: Combine like terms

Combine the like terms to simplify the expression: \[ A = 15x^2 + (20x - 24x) - 32 \] \[ A = 15x^2 - 4x - 32 \]

Final Answer

The polynomial that represents the area of the rectangle is: \[ 15x^2 - 4x - 32 \]

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