4. Consider the figure below. (5x - 14) ft
(2x) - 5x2 - 12x + 14) ft
What is the total area, in square feet, of the figure

(10x⁴ - 52x³ + 5x² + 246x - 196) ft²

Step-by-step explanation:

The figure can be divided into two rectangles: the small rectangle and the large rectangle.

Dimensions of the small rectangle:

Length (l) = (x) ft

Width (w) = (x² - 6) - (5x - 14) = x² - 6 - 5x + 14 = (x² - 5x + 8) ft

Area of small rectangle = l*w = (x)(x² - 5x + 8)

Area = x(x²) - x(5x) + x(8) (using distributive property)

Area of small rectangle = (x³ - 5x² + 8x) ft²

Dimensions of large rectangle:

Length (l) = (2x³ - 5x² - 12x + 14) ft

Width (w) = (5x - 14) ft

Area of large rectangle = l*w = (2x³ - 5x² - 12x + 14)(5x - 14)

2x³(5x - 14) - 5x²(5x - 14) - 12x(5x - 14) + 14(5x - 14) (distributive property)

10x⁴ - 28x³ - 25x³ + 70x² - 60x² + 168x + 70x - 196

Combine like terms

Area of large rectangle = (10x⁴ - 53x³ + 10x² + 238x - 196) ft²

Area of figure = area of small rectangle + area of large rectangle

= (x³ - 5x² + 8x) + (10x⁴ - 53x³ + 10x² + 238x - 196)

Open parentheses

= x³ - 5x² + 8x + 10x⁴ - 53x³ + 10x² + 238x - 196

Combine like terms and arrange in standard form (from the greatest degree to the least)

= 10x⁴ + x³ - 53x³ - 5x² + 10x² + 8x + 238x - 196

= 10x⁴ - 52x³ + 5x² + 246x - 196

Area of the figure = (10x⁴ - 52x³ + 5x² + 246x - 196) ft²

30005

yes ok