Final answer:
The area of a rectangle whose length is (3x - 1) and width is (2x² - 4x + 5) is calculated by multiplying the length by the width to get 6x³ - 14x² + 19x - 5.
Step-by-step explanation:
To find the area of a rectangle, the formula to use is length multiplied by width. Given that the length of the rectangle is (3x - 1) and the width is (2x² - 4x + 5), we apply this formula by multiplying these two expressions:
Area = Length × Width
Area = (3x - 1) × (2x² - 4x + 5)
Expanding the expression, we get:
Area = (3x × 2x²) + (3x × -4x) + (3x × 5) + (-1 × 2x²) + (-1 × -4x) + (-1 × 5)
Area = (6x³ - 12x² + 15x - 2x² + 4x - 5)
Combining like terms, we get:Area = 6x³ - 14x² + 19x - 5
This is the area of the rectangle in terms of x.