Cho hai đa thức P(x) = 7x^3 - 8x + 12 và Q(x) = 6x^2 - 2x^3 + 3x - 5. Hãy tính P(x) + Q(x) bằng hai cách.

Cách 1:

P(x) + Q(x) = (7x³ - 8x + 12) + (6x² - 2x³ + 3x - 5)

P(x) + Q(x) = 7x³ - 8x + 12 + 6x² - 2x³ + 3x - 5

P(x) + Q(x) = (7x³ - 2x³) + 6x² + (-8x + 3x) + (12 - 5)

P(x) + Q(x) = 5x³ + 6x² - 5x + 7

Vậy P(x) + Q(x) = 5x³ + 6x² - 5x + 7.

Cách 2:

Q(x) = 6x² - 2x³ + 3x - 5 = -2x³ + 6x² + 3x - 5.

Khi đó thực hiện đặt phép tính ta có:

$\begin{array}{l}\underset{¯}{+\begin{array}{c}\begin{array}{l}\\ -\end{array}\end{array}\begin{array}{c}\begin{array}{l}7{\text{x}}^3\\ 2{\text{x}}^3\end{array}\end{array}\begin{array}{c}\begin{array}{l}\\ +\end{array}\end{array}\begin{array}{c}\begin{array}{l}\\ 6{\text{x}}^2\end{array}\end{array}\begin{array}{c}\begin{array}{l}-\\ +\end{array}\end{array}\begin{array}{c}\begin{array}{l}8\text{x}\\ 3\text{x}\end{array}\end{array}\begin{array}{c}\begin{array}{l}+\\ -\end{array}\end{array}\begin{array}{c}\begin{array}{l}12\\ 5\end{array}\end{array}}\\ 5{\text{x}}^3+6{\text{x}}^2-5\text{x}+7\end{array}$

Vậy P(x) + Q(x) = 5x³ + 6x² - 5x + 7.