(3x³ - 19x² + 10x + 50) ÷ (x - 5) =?
- 3x² + 4x + 10
- 3x² - 4x - 10
- 3x² - 4x + 10
- None of these
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
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