Question

Use synthetic division to solve (x4 – 1) ÷ (x – 1). What is the quotient?
x cubed minus x squared + x minus 1
x3
x cubed + x squared + x + 1
x3 – 2

Answer 1

Divide x^4 − 1 by x − 1 using synthetic division with root 1.

Coefficients: 1, 0, 0, 0, −1

Synthetic steps:
- Bring down 1
- Multiply by 1 → 1; add → 1
- Multiply by 1 → 1; add → 1
- Multiply by 1 → 1; add → 1
- Multiply by 1 → 1; add → 0 (remainder)

Quotient coefficients: 1, 1, 1, 1 → quotient = x^3 + x^2 + x + 1.