Wykonaj dzielenie wielomianów:- Zadanie 8.123: Matematyka 2. Zakres rozszerzony

Rozwiązanie

$(6 x^{3} + 13 x^{2} + x - 2) : (x^{2} + \frac{5}{2} x + 1) = 6 x - 2$

$- \underline{06 x - 2000000000000} - (6 x^{3} + 13 x^{2} + x - 2) : (x^{2} + \frac{5}{2} x + 1) \underline{- 6 x^{3} - 15 x^{2} - 6 x} 0000 - 2 x^{2} - 5 x - 2 000000 \underline{2 x^{2} + 5 x + 2} - 0000000000000000$

$(8 x^{3} - 6 x^{2} - 17 x - 6) : (8 x^{2} - 10 x - 12) = x + \frac{1}{2}$

$- 0 \underline{0 x + \frac{1}{2} 000000000000} - (8 x^{3} - 6 x^{2} - 17 x - 6) : (8 x^{2} - 10 x - 12) \underline{- 8 x^{3} + 10 x^{2} + 12 x} 0000004 x^{2} - 5 x - 6 00000 \underline{- 4 x^{2} + 5 x + 6} - 0000000000000000$

$(24 x^{3} - 26 x^{2} + 9 x - 1) : (12 x^{2} - 7 x + 1) = 2 x - 1$

$- \underline{002 x - 1000000000000} - (24 x^{3} - 26 x^{2} + 9 x - 1) : (12 x^{2} - 7 x + 1) \underline{- 24 x^{3} + 14 x^{2} - 2 x} 00000 - 12 x^{2} + 7 x - 1 0000000 \underline{12 x^{2} - 7 x + 1} - 000000000000000000$

$(12 x^{3} + 16 x^{2} + 7 x + 1) : (x + \frac{1}{2})^{2} = (12 x^{3} + 16 x^{2} + 7 x + 1) : (x^{2} + x + \frac{1}{4}) = 12 x + 4$

$- \underline{012 x + 4000000000000} - (12 x^{3} + 16 x^{2} + 7 x + 1) : (x^{2} + x + \frac{1}{4}) \underline{- 12 x^{3} - 12 x^{2} - 3 x} 00000004 x^{2} + 4 x + 1 000000 \underline{- 4 x^{2} - 4 x - 1} - 00000000000000000$