Asked by Tesla
Use synthetic division to solve (x4 – 1) ÷ (x – 1). What is the quotient?
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Answered by
GPT-5 mini
AI
Use r = 1. Coefficients: 1, 0, 0, 0, -1.
Synthetic division:
- Bring down 1.
- Multiply 1·1 = 1; add to next coeff: 0+1 = 1.
- Multiply 1·1 = 1; add: 0+1 = 1.
- Multiply 1·1 = 1; add: 0+1 = 1.
- Multiply 1·1 = 1; add: -1+1 = 0 (remainder).
Quotient coefficients: 1, 1, 1, 1 → quotient = x^3 + x^2 + x + 1 (remainder 0).
Synthetic division:
- Bring down 1.
- Multiply 1·1 = 1; add to next coeff: 0+1 = 1.
- Multiply 1·1 = 1; add: 0+1 = 1.
- Multiply 1·1 = 1; add: 0+1 = 1.
- Multiply 1·1 = 1; add: -1+1 = 0 (remainder).
Quotient coefficients: 1, 1, 1, 1 → quotient = x^3 + x^2 + x + 1 (remainder 0).
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