Explanation

To divide (3x³ - 19x² + 10x + 50) by (x - 5), let's perform polynomial division:

1. Divide 3x³ by x: 3x²

2. Multiply (x - 5) by 3x²: 3x³ - 15x²

3. Subtract: -19x² + 15x² = -4x², bring down 10x

4. Divide -4x² by x: -4x

5. Multiply (x - 5) by -4x: -4x² + 20x

6. Subtract: 10x - 20x = -10x, bring down 50

7. Divide -10x by x: -10

8. Multiply (x - 5) by -10: -10x + 50

9. Subtract: 0

The quotient is:

3x² - 4x - 10