Algebra Esempi

$\frac{- 2 x^{12} + 3 x^{6} - x^{5} + 15 x}{x^{5}}$

Passaggio 1

Imposta i polinomi da dividere. Se non c'è un termine per ogni esponente, inseriscine uno con un valore di $0$ .

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

Passaggio 2

Dividi il termine di ordine più alto nel dividendo $- 2 x^{12}$ per il termine di ordine più alto nel divisore $x^{5}$ .

$2 x^{7}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

Passaggio 3

Moltiplica il nuovo quoziente per il divisore.

$2 x^{7}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

Passaggio 4

L'espressione deve essere sottratta dal dividendo; quindi, cambia tutti i segni in $- 2 x^{12} + 0 + 0 + 0 + 0 + 0$

$2 x^{7}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

Passaggio 5

Dopo aver cambiato i segni, somma l'ultimo dividendo del polinomio moltiplicato per trovare il nuovo dividendo.

$2 x^{7}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

Passaggio 6

Abbassa i termini successivi dal dividendo originale nel dividendo attuale.

$2 x^{7}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

Passaggio 7

Dividi il termine di ordine più alto nel dividendo $3 x^{6}$ per il termine di ordine più alto nel divisore $x^{5}$ .

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

Passaggio 8

Moltiplica il nuovo quoziente per il divisore.

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

Passaggio 9

L'espressione deve essere sottratta dal dividendo; quindi, cambia tutti i segni in $3 x^{6} + 0 + 0 + 0 + 0 + 0$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

Passaggio 10

Dopo aver cambiato i segni, somma l'ultimo dividendo del polinomio moltiplicato per trovare il nuovo dividendo.

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

Passaggio 11

Abbassa i termini successivi dal dividendo originale nel dividendo attuale.

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

$0$

Passaggio 12

Dividi il termine di ordine più alto nel dividendo $- x^{5}$ per il termine di ordine più alto nel divisore $x^{5}$ .

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$1$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

$0$

Passaggio 13

Moltiplica il nuovo quoziente per il divisore.

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$1$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

$0$

$x^{5}$

$0$

Passaggio 14

L'espressione deve essere sottratta dal dividendo; quindi, cambia tutti i segni in $- x^{5} + 0 + 0 + 0 + 0 + 0$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$1$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

$0$

$x^{5}$

$0$

Passaggio 15

Dopo aver cambiato i segni, somma l'ultimo dividendo del polinomio moltiplicato per trovare il nuovo dividendo.

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$1$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

$0$

$x^{5}$

$0$

$15 x$

$0$

Passaggio 16

La risposta finale è il quoziente più il resto sopra il divisore.

$- 2 x^{7} + 3 x - 1 + \frac{15 x}{x^{5}}$