Question

Use synthetic division to solve (x3 + 1) = (x - 1). What is the quotient?

x² + x + 1 + 1 2 3
x2-x+1
x2+x+1+2
x3 - x2 + x

Answer 1

Synthetic division yields

1 | 1 0 0 1

. | 1 1 1

= = = = = = = = = =

. | 1 1 1 2

which translates to

(x³ + 1) / (x - 1) = x² + x + 1 + 2/(x - 1)

where the quotient is x² + x + 1.