Question

which polynomial represents the area of the rectangle?
4x² + 2x - 6
4x² - 6
4x² - 10x - 6
4x² - 2x - 6

Explanation:

Step1: Recall area of rectangle formula

The area \( A \) of a rectangle is given by the product of its length and width, i.e., \( A = \text{length} \times \text{width} \). Here, the length is \( 4x - 6 \) and the width is \( x + 1 \). So we need to compute \( (4x - 6)(x + 1) \).

Step2: Apply distributive property (FOIL method)

First, multiply the First terms: \( 4x \times x = 4x^2 \).
Then, multiply the Outer terms: \( 4x \times 1 = 4x \).
Next, multiply the Inner terms: \( -6 \times x = -6x \).
Finally, multiply the Last terms: \( -6 \times 1 = -6 \).

Now, combine these terms: \( 4x^2 + 4x - 6x - 6 \).

Step3: Combine like terms

Combine the \( x \)-terms: \( 4x - 6x = -2x \). So the polynomial becomes \( 4x^2 - 2x - 6 \).

Answer:

\( 4x^2 - 2x - 6 \) (the fourth option)