Tính: a) (x2 + 2x + 3) + (3x2 - 5x + 1); b) (4x3 - 2x2 - 6) - (x3 - 7x2 + x - 5); c) -3x2(6x2 - 8x + 1)

a) (x² + 2x + 3) + (3x² - 5x + 1)

= x² + 2x + 3 + 3x² - 5x + 1

= (x² + 3x²) + (2x - 5x) + (3 + 1)

= 4x² - 3x + 4.

b) (4x³ - 2x² - 6) - (x³ - 7x² + x - 5)

= 4x³ - 2x² - 6 - x³ + 7x² - x + 5

= (4x³ - x³) + (-2x² + 7x²) - x + (-6 + 5)

= 3x³ + 5x² - x - 1.

c) -3x²(6x² - 8x + 1)

= -3x² . 6x² - (-3x²) . 8x + (-3x²) . 1

= -18x⁴ - (-24x³) - 3x²

= - 18x⁴ + 24x³ - 3x².

d) (4x² + 2x + 1)(2x - 1)

= 4x² . 2x - 4x² . 1 + 2x . 2x - 2x . 1 + 1 . 2x - 1.1

= 8x³ - 4x² + 4x² - 2x + 2x - 1

= 8x³ - 1.

e) (x⁶ - 2x⁴ + x²) : (-2x²)

= x⁶ : (-2x²) - 2x⁴ : (-2x²) + x² : (-2x²)

= $\frac{-1}{2}$x⁴ - (-x²) + $\left(\frac{-1}{2}\right)$

= $\frac{-1}{2}$x⁴ + x² - $\frac{1}{2}$.

g) Thực hiện phép tính ta được:

$\begin{array}{cccccc}& x^5& -& x^4& -& 2{\text{x}}^3\\ \overline{}& x^5& +& x^4& & \\ & & & -2{\text{x}}^4& -& 2{\text{x}}^3\\ & & \overline{}& -2{\text{x}}^4& -& 2{\text{x}}^3\\ & & & & & 0\end{array}\begin{array}{ccc}{x}^2& +& x\\ x^3& -& 2{\text{x}}^2\\ & & \\ & & \\ & & \end{array}$

Vậy (x⁵ - x⁴ - 2x³) : (x² + x) = x³ - 2x².