Álgebra Exemplos

$\frac{5 x^{10} - 9 x^{8} - 9 x^{5} + 7 x}{x^{5}}$

Etapa 1

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

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

Etapa 2

Divida o termo de ordem mais alta no dividendo $5 x^{10}$ pelo termo de ordem mais alta no divisor $x^{5}$ .

$5 x^{5}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

Etapa 3

Multiplique o novo termo do quociente pelo divisor.

$5 x^{5}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

Etapa 4

A expressão precisa ser subtraída do dividendo. Portanto, altere todos os sinais em $5 x^{10} + 0 + 0 + 0 + 0 + 0$ .

$5 x^{5}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

Etapa 5

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

$5 x^{5}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

$9 x^{8}$

$0$

$9 x^{5}$

Etapa 6

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

$5 x^{5}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

$9 x^{8}$

$0$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

Etapa 7

Divida o termo de ordem mais alta no dividendo $- 9 x^{8}$ pelo termo de ordem mais alta no divisor $x^{5}$ .

$5 x^{5}$

$0 x^{4}$

$9 x^{3}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

$9 x^{8}$

$0$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

Etapa 8

Multiplique o novo termo do quociente pelo divisor.

$5 x^{5}$

$0 x^{4}$

$9 x^{3}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

$9 x^{8}$

$0$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$9 x^{8}$

$0$

Etapa 9

A expressão precisa ser subtraída do dividendo. Portanto, altere todos os sinais em $- 9 x^{8} + 0 + 0 + 0 + 0 + 0$ .

$5 x^{5}$

$0 x^{4}$

$9 x^{3}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

$9 x^{8}$

$0$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$9 x^{8}$

$0$

Etapa 10

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

$5 x^{5}$

$0 x^{4}$

$9 x^{3}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

$9 x^{8}$

$0$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$9 x^{8}$

$0$

$9 x^{5}$

$0$

Etapa 11

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

$5 x^{5}$

$0 x^{4}$

$9 x^{3}$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

$9 x^{8}$

$0$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$9 x^{8}$

$0$

$9 x^{5}$

$0$

$0 x^{2}$

$7 x$

$0$

Etapa 12

Divida o termo de ordem mais alta no dividendo $- 9 x^{5}$ pelo termo de ordem mais alta no divisor $x^{5}$ .

$5 x^{5}$

$0 x^{4}$

$9 x^{3}$

$0 x^{2}$

$0 x$

$9$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

$9 x^{8}$

$0$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$9 x^{8}$

$0$

$9 x^{5}$

$0$

$0 x^{2}$

$7 x$

$0$

Etapa 13

Multiplique o novo termo do quociente pelo divisor.

$5 x^{5}$

$0 x^{4}$

$9 x^{3}$

$0 x^{2}$

$0 x$

$9$

$x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{10}$

$0 x^{9}$

$9 x^{8}$

$0 x^{7}$

$0 x^{6}$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$0$

$5 x^{10}$

$0$

$9 x^{8}$

$0$

$9 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$7 x$

$9 x^{8}$

$0$

$9 x^{5}$

$0$

$0 x^{2}$

$7 x$

$0$

$9 x^{5}$

$0$

Etapa 14

A expressão precisa ser subtraída do dividendo. Portanto, altere todos os sinais em $- 9 x^{5} + 0 + 0 + 0 + 0 + 0$ .

												$5 x^{5}$	+	$0 x^{4}$	-	$9 x^{3}$	+	$0 x^{2}$	+	$0 x$	-	$9$
$x^{5}$	+	$0 x^{4}$	+	$0 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$		$5 x^{10}$	+	$0 x^{9}$	-	$9 x^{8}$	+	$0 x^{7}$	+	$0 x^{6}$	-	$9 x^{5}$	+	$0 x^{4}$	+	$0 x^{3}$	+	$0 x^{2}$	+	$7 x$	+	$0$
											-	$5 x^{10}$	-	$0$	-	$0$	-	$0$	-	$0$	-	$0$
															-	$9 x^{8}$	+	$0$	+	$0$	-	$9 x^{5}$	+	$0 x^{4}$	+	$0 x^{3}$	+	$0 x^{2}$	+	$7 x$
															+	$9 x^{8}$	-	$0$	-	$0$	-	$0$	-	$0$	-	$0$
																					-	$9 x^{5}$	+	$0$	+	$0$	+	$0 x^{2}$	+	$7 x$	+	$0$
																					+	$9 x^{5}$	-	$0$	-	$0$	-	$0$	-	$0$	-	$0$

Etapa 15

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

												$5 x^{5}$	+	$0 x^{4}$	-	$9 x^{3}$	+	$0 x^{2}$	+	$0 x$	-	$9$
$x^{5}$	+	$0 x^{4}$	+	$0 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$		$5 x^{10}$	+	$0 x^{9}$	-	$9 x^{8}$	+	$0 x^{7}$	+	$0 x^{6}$	-	$9 x^{5}$	+	$0 x^{4}$	+	$0 x^{3}$	+	$0 x^{2}$	+	$7 x$	+	$0$
											-	$5 x^{10}$	-	$0$	-	$0$	-	$0$	-	$0$	-	$0$
															-	$9 x^{8}$	+	$0$	+	$0$	-	$9 x^{5}$	+	$0 x^{4}$	+	$0 x^{3}$	+	$0 x^{2}$	+	$7 x$
															+	$9 x^{8}$	-	$0$	-	$0$	-	$0$	-	$0$	-	$0$
																					-	$9 x^{5}$	+	$0$	+	$0$	+	$0 x^{2}$	+	$7 x$	+	$0$
																					+	$9 x^{5}$	-	$0$	-	$0$	-	$0$	-	$0$	-	$0$
																													+	$7 x$	+	$0$

Etapa 16

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

$5 x^{5} - 9 x^{3} - 9 + \frac{7 x}{x^{5}}$