Let me work through this polynomial division problem step by step to verify the solution shown.
Problem: Divide (x³ - 5x² + 9x - 5) by (x - 1)
Step-by-step verification:
1.
First term: x³ ÷ x = x²
- Multiply: x²(x - 1) = x³ - x²
- Subtract: (x³ - 5x²) - (x³ - x²) = -4x² ✓
2.
Bring down 9x: We have -4x² + 9x
- Second term: -4x² ÷ x = -4x
- Multiply: -4x(x - 1) = -4x² + 4x
- Subtract: (-4x² + 9x) - (-4x² + 4x) = 5x ✓
3.
Bring down -5: We have 5x - 5
- Third term: 5x ÷ x = 5
- Multiply: 5(x - 1) = 5x - 5
- Subtract: (5x - 5) - (5x - 5) = 0 ✓
Verification by multiplication:
Let's check if (x - 1)(x² - 4x + 5) = x³ - 5x² + 9x - 5
(x - 1)(x² - 4x + 5)
= x(x² - 4x + 5) - 1(x² - 4x + 5)
= x³ - 4x² + 5x - x² + 4x - 5
= x³ - 5x² + 9x - 5 ✓
The calculation is correct!
Final Answer:
x² - 4x + 5
Parent Tip: Review the logic above to help your child master the concept of factoring cubic polynomials worksheet.
