1. (8x^3+12x^2-6x+4) : (4x^2-2x+1) 2. (x^4+x^2-4+2x^3) : (x+2)

Разложим числитель на множители и сократим дробь:

1.

f (x) = 8x³ + 12x² - 6x + 4; g (x) = 4x² - 2x + 1; f (x) = 2x (4x² - 2x + 1) + 16x² - 8x + 4; f (x) = 2x (4x² - 2x + 1) + 4 (4x² - 2x + 1); f (x) = (4x² - 2x + 1) (2x + 4); f (x) / g (x) = 2x + 4; (8x³ + 12x² - 6x + 4) / (4x² - 2x + 1) = 2x + 4.

2.

f (x) = x⁴ + x² - 4 + 2x³; g (x) = x + 2; f (x) = x³ (x + 2) + (x + 2) (x - 2); f (x) = (x + 2) (x³ + x - 2); f (x) / g (x) = x³ + x - 2; (x⁴ + x² - 4 + 2x³) / (x + 2) = x³ + x - 2.

Ответ:

1. 2x + 4; 2. x³ + x - 2.