Tính: a) (x^3 + 1) : (x^2 - x + 1); b) (8x^3 - 6x^2 + 5) : (x^2 + x + 1).

a) Thực hiện phép chia ta được:

$\begin{array}{cccccccc}& x^3& & & & & +& 1\\ \overline{}& x^3& -& x^2& +& x& & \\ & & & x^2& -& x& +& 1\\ & & \overline{}& x^2& -& x& +& 1\\ & & & & & & & 0\end{array}\begin{array}{ccccc}{x}^2& -& x& +& 1\\ x& +& 1& & \\ & & & & \\ & & & & \\ & & & & \end{array}$

Vậy (x3 + 1) : (x2 - x + 1) = x + 1.

b) Thực hiện phép chia ta được:

$\begin{array}{cccccccc}& 8x^3& -& 6{\text{x}}^2& & & +& 5\\ \overline{}& 8{\text{x}}^3& +& 8{\text{x}}^2& +& 8\text{x}& & \\ & & -& 14{\text{x}}^2& -& 8\text{x}& +& 5\\ & \overline{}& -& 14{\text{x}}^2& -& 14\text{x}& -& 14\\ & & & & & \text{6x}& +& 19\end{array}\begin{array}{ccccc}{x}^2& +& x& +& 1\\ 8\text{x}& -& 14& & \\ & & & & \\ & & & & \\ & & & & \end{array}$

Vậy 8x3 - 6x2 + 5 = (8x - 14) . (x2 + x + 1) + (6x + 19).