Tính: a) (x^2 - 2x + 1) : (x - 1); b) (x^3 + 2x^2 + x) : (x^2 + x); c) (-16x^4 + 1) : (-4x^2 + 1); d) (-32x^5 + 1) : (-2x + 1).

a) Thực hiện phép tính ta được:

$\begin{array}{cccccc}& x^2& -& 2\text{x}& +& 1\\ \overline{}& x^2& -& x& & \\ & & -& x& +& 1\\ & \overline{}& -& x& +& 1\\ & & & & & 0\end{array}\begin{array}{ccc}x& -& 1\\ x& -& 1\\ & & \\ & & \\ & & \end{array}$

Vậy (x2 - 2x + 1) : (x - 1) = x - 1.

b) Thực hiện phép tính ta được:

$\begin{array}{cccccc}& x^3& +& 2{\text{x}}^2& +& x\\ \overline{}& x^3& +& x^2& & \\ & & & x^2& +& x\\ & & \overline{}& x^2& +& x\\ & & & & & 0\end{array}\begin{array}{ccc}{x}^2& +& x\\ x& +& 1\\ & & \\ & & \\ & & \end{array}$

Vậy (x3 + 2x2 + x) : (x2 + x) = x + 1.

c) Thực hiện phép tính ta được:

$\begin{array}{cccccc}& -16{\text{x}}^4& & & +& 1\\ \overline{}& -16{\text{x}}^4& +& 4{\text{x}}^2& & \\ & & & -4{\text{x}}^2& +& 1\\ & & \overline{}& -4{\text{x}}^2& +& 1\\ & & & & & 0\end{array}\begin{array}{ccc}-4{\text{x}}^2& +& 1\\ 4{\text{x}}^2& +& 1\\ & & \\ & & \\ & & \end{array}$

Vậy (-16x4 + 1) : (-4x2 + 1) = 4x2 + 1.

d) Thực hiện phép tính ta được:

$\begin{array}{cccccccccccc}& -32{\text{x}}^5& & & & & & & & & +& 1\\ \overline{}& -32{\text{x}}^5& +& 16{\text{x}}^4& & & & & & & & \\ & & & -16{\text{x}}^4& & & & & & & +& 1\\ & & \overline{}& -16{\text{x}}^4& +& 8{\text{x}}^3& & & & & & \\ & & & & & -8{\text{x}}^3& & & & & +& 1\\ & & & & \overline{}& -8{\text{x}}^3& +& 4{\text{x}}^2& & & & \\ & & & & & & & -4{\text{x}}^2& & & +& 1\\ & & & & & & \overline{}& -4{\text{x}}^2& +& 2\text{x}& & \\ & & & & & & & & & -2\text{x}& +& 1\\ & & & & & & & & \overline{}& -2\text{x}& +& 1\\ & & & & & & & & & & & 0\end{array}\begin{array}{ccccccccc}-2\text{x}& +& 1& & & & & & \\ 16{\text{x}}^4& +& 8{\text{x}}^3& +& 4{\text{x}}^2& +& 2\text{x}& +& 1\\ & & & & & & & & \\ & & & & & & & & \\ & & & & & & & & \\ & & & & & & & & \\ & & & & & & & & \\ & & & & & & & & \\ & & & & & & & & \\ & & & & & & & & \\ & & & & & & & & \end{array}$

Vậy (-32x5 + 1) : (-2x + 1) = 16x4 + 8x3 + 4x2 + 2x + 1.