Final answer:
To find the length of the rectangle, we can use the formula for the area of a rectangle: Area = length × width. In this case, the area is given as x³ - 21x² + 147x - 343 and the width is x - 7. So, we can set up the equation (x³ - 21x² + 147x - 343) = (x - 7) × length and solve for the value of length.
Step-by-step explanation:
To find the length of the rectangle, we can use the formula for the area of a rectangle: Area = length × width. In this case, the area is given as x³ - 21x² + 147x - 343 and the width is x - 7. So, we can set up the equation: (x³ - 21x² + 147x - 343) = (x - 7) × length. We can solve this equation to find the value of length.
Expanding the equation, we have: x³ - 21x² + 147x - 343 = x × length - 7 × length.
Now, we can group the terms and solve for length:
x³ - x × length = - 147x + 7 × length - 343.
Subtracting x³ from both sides, we get: - x × length = - 147x + 7 × length - 343.
Next, we can combine like terms and solve for length:
- x × length - 7 × length = - 147x - 343.
Factoring out the common factors, we have: length × (- x - 7) = - 147x - 343.
Dividing both sides by (- x - 7), we find: length = (- 147x - 343) / (- x - 7).