Question

the formula for the area of a parallelogram is a = bh, where b is the base and h is the height.
(2x²+2x−6) cm
(x−4) cm
(not drawn to scale)
which simplified expression represents the area of the parallelogram?
○ −4x³ + 14x − 24 square centimeters
○ 2x³ − 6x² − 14x + 24 square centimeters
○ −4x³ − 14x + 24 square centimeters
○ 2x³ + 6x² + 14x + 24 square centimeters

Explanation:

Step1: Identify base and height

Base \( b = (2x^2 + 2x - 6) \) cm, height \( h = (x - 4) \) cm. Area \( A = bh \), so multiply the two polynomials.

Step2: Multiply the polynomials

Use distributive property (FOIL for polynomials):
\( (2x^2 + 2x - 6)(x - 4) = 2x^2(x - 4) + 2x(x - 4) - 6(x - 4) \)
\( = 2x^3 - 8x^2 + 2x^2 - 8x - 6x + 24 \)

Step3: Combine like terms

Combine \( -8x^2 + 2x^2 = -6x^2 \), \( -8x - 6x = -14x \):
\( 2x^3 - 6x^2 - 14x + 24 \)

Answer:

2x³ - 6x² - 14x + 24 square centimeters (corresponding to the second option: 2x³ - 6x² - 14x + 24 square centimeters)