기초 대수 예제

$\frac{x^{12} - 2 x^{7} + 6 x^{2} - 4}{x + 1}$

단계 1

다항식을 나눗셈 형태로 적습니다. 각 지수에 대하여 항이 없는 경우 값이 $0$ 인 항을 삽입합니다.

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

단계 2

피제수 $x^{12}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

단계 3

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

단계 4

식을 피제수에서 빼야 하므로 $x^{12} + x^{11}$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

단계 5

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

단계 6

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

단계 7

피제수 $- x^{11}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

단계 8

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

단계 9

식을 피제수에서 빼야 하므로 $- x^{11} - x^{10}$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

단계 10

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

단계 11

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x^{10}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

단계 12

피제수 $x^{10}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

단계 13

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

단계 14

식을 피제수에서 빼야 하므로 $x^{10} + x^{9}$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

단계 15

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

단계 16

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

단계 17

피제수 $- x^{9}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

단계 18

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

단계 19

식을 피제수에서 빼야 하므로 $- x^{9} - x^{8}$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

단계 20

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

단계 21

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

단계 22

피제수 $x^{8}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

단계 23

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

단계 24

식을 피제수에서 빼야 하므로 $x^{8} + x^{7}$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

단계 25

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

단계 26

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

단계 27

피제수 $- 3 x^{7}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

단계 28

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

단계 29

식을 피제수에서 빼야 하므로 $- 3 x^{7} - 3 x^{6}$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

단계 30

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

단계 31

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

단계 32

피제수 $3 x^{6}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

단계 33

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

단계 34

식을 피제수에서 빼야 하므로 $3 x^{6} + 3 x^{5}$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

단계 35

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

단계 36

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

단계 37

피제수 $- 3 x^{5}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

단계 38

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

단계 39

식을 피제수에서 빼야 하므로 $- 3 x^{5} - 3 x^{4}$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

단계 40

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

단계 41

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

단계 42

피제수 $3 x^{4}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

단계 43

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

단계 44

식을 피제수에서 빼야 하므로 $3 x^{4} + 3 x^{3}$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

단계 45

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

단계 46

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

단계 47

피제수 $- 3 x^{3}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

단계 48

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

단계 49

식을 피제수에서 빼야 하므로 $- 3 x^{3} - 3 x^{2}$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

단계 50

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

단계 51

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

단계 52

피제수 $9 x^{2}$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

단계 53

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

단계 54

식을 피제수에서 빼야 하므로 $9 x^{2} + 9 x$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

단계 55

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

단계 56

원래 피제수의 다음 항을 아래로 내려 현재 피제수로 보냅니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

$4$

단계 57

피제수 $- 9 x$ 의 고차항을 제수 $x$ 의 고차항으로 나눕니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$9$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

$4$

단계 58

새로운 몫 값에 제수를 곱합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$9$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

$4$

$9 x$

$9$

단계 59

식을 피제수에서 빼야 하므로 $- 9 x - 9$ 의 모든 부호를 바꿉니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$9$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

$4$

$9 x$

$9$

단계 60

부호를 바꾼 뒤, 곱한 다항식의 마지막 피제수를 더해 새로운 피제수를 구합니다.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$9$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

$4$

$9 x$

$9$

$5$

단계 61

최종 답은 몫에 제수 분의 나머지를 더한 값입니다.

$x^{11} - x^{10} + x^{9} - x^{8} + x^{7} - 3 x^{6} + 3 x^{5} - 3 x^{4} + 3 x^{3} - 3 x^{2} + 9 x - 9 + \frac{5}{x + 1}$