Álgebra Exemplos

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

Etapa 1

Estabeleça os polinômios a serem divididos. Se não houver um termo para cada expoente, insira um com valor de $0$ .

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

Etapa 2

Divida o termo de ordem mais alta no dividendo $- 2 x^{12}$ pelo termo de ordem mais alta no divisor $x^{5}$ .

$2 x^{7}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

Etapa 3

Multiplique o novo termo do quociente pelo divisor.

$2 x^{7}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

Etapa 4

A expressão precisa ser subtraída do dividendo. Portanto, altere todos os sinais em $- 2 x^{12} + 0 + 0 + 0 + 0 + 0$ .

$2 x^{7}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

Etapa 5

Depois de alterar os sinais, some o último dividendo do polinômio multiplicado para encontrar o novo dividendo.

$2 x^{7}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

Etapa 6

Tire os próximos termos do dividendo original e os coloque no dividendo atual.

$2 x^{7}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

Etapa 7

Divida o termo de ordem mais alta no dividendo $3 x^{6}$ pelo termo de ordem mais alta no divisor $x^{5}$ .

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

Etapa 8

Multiplique o novo termo do quociente pelo divisor.

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

Etapa 9

A expressão precisa ser subtraída do dividendo. Portanto, altere todos os sinais em $3 x^{6} + 0 + 0 + 0 + 0 + 0$ .

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

Etapa 10

Depois de alterar os sinais, some o último dividendo do polinômio multiplicado para encontrar o novo dividendo.

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

Etapa 11

Tire os próximos termos do dividendo original e os coloque no dividendo atual.

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

$0$

Etapa 12

Divida o termo de ordem mais alta no dividendo $- x^{5}$ pelo termo de ordem mais alta no divisor $x^{5}$ .

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$1$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

$0$

Etapa 13

Multiplique o novo termo do quociente pelo divisor.

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$1$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

$0$

$x^{5}$

$0$

Etapa 14

A expressão precisa ser subtraída do dividendo. Portanto, altere todos os sinais em $- x^{5} + 0 + 0 + 0 + 0 + 0$ .

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$1$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

$0$

$x^{5}$

$0$

Etapa 15

Depois de alterar os sinais, some o último dividendo do polinômio multiplicado para encontrar o novo dividendo.

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$3 x$

$1$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$0$

$2 x^{12}$

$0$

$3 x^{6}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$15 x$

$3 x^{6}$

$0$

$x^{5}$

$0$

$15 x$

$0$

$x^{5}$

$0$

$15 x$

$0$

Etapa 16

A resposta final é o quociente mais o resto sobre o divisor.

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