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인기 있는 대수학 >

확장 (X-1)(X-2)(X-3)(X-4)(X-5)(X-6)(X-7)(X-8)(X-9)(X-10)(X-11)

해법

확장

(X - 1) (X - 2) (X - 3) (X - 4) (X - 5) (X - 6) (X - 7) (X - 8) (X - 9) (X - 10) (X - 11)

해법

X^{11} - 66 X^{10} + 1925 X^{9} - 32670 X^{8} + 357423 X^{7} - 2637558 X^{6} + 13339535 X^{5} - 45995730 X^{4} + 105258076 X^{3} - 150917976 X^{2} + 120543840 X - 39916800

솔루션 단계

(X - 1) (X - 2) (X - 3) (X - 4) (X - 5) (X - 6) (X - 7) (X - 8) (X - 9) (X - 10) (X - 11)

(X - 1) (X - 2)

확대한다:

X^{2} - 3 X + 2

= (X^{2} - 3 X + 2) (X - 3) (X - 4) (X - 5) (X - 6) (X - 7) (X - 8) (X - 9) (X - 10) (X - 11)

(X^{2} - 3 X + 2) (X - 3)

확대한다:

X^{3} - 6 X^{2} + 11 X - 6

= (X^{3} - 6 X^{2} + 11 X - 6) (X - 4) (X - 5) (X - 6) (X - 7) (X - 8) (X - 9) (X - 10) (X - 11)

(X^{3} - 6 X^{2} + 11 X - 6) (X - 4)

확대한다:

X^{4} - 10 X^{3} + 35 X^{2} - 50 X + 24

= (X^{4} - 10 X^{3} + 35 X^{2} - 50 X + 24) (X - 5) (X - 6) (X - 7) (X - 8) (X - 9) (X - 10) (X - 11)

(X^{4} - 10 X^{3} + 35 X^{2} - 50 X + 24) (X - 5)

확대한다:

X^{5} - 15 X^{4} + 85 X^{3} - 225 X^{2} + 274 X - 120

= (X^{5} - 15 X^{4} + 85 X^{3} - 225 X^{2} + 274 X - 120) (X - 6) (X - 7) (X - 8) (X - 9) (X - 10) (X - 11)

(X^{5} - 15 X^{4} + 85 X^{3} - 225 X^{2} + 274 X - 120) (X - 6)

확대한다:

X^{6} - 21 X^{5} + 175 X^{4} - 735 X^{3} + 1624 X^{2} - 1764 X + 720

= (X^{6} - 21 X^{5} + 175 X^{4} - 735 X^{3} + 1624 X^{2} - 1764 X + 720) (X - 7) (X - 8) (X - 9) (X - 10) (X - 11)

(X^{6} - 21 X^{5} + 175 X^{4} - 735 X^{3} + 1624 X^{2} - 1764 X + 720) (X - 7)

확대한다:

X^{7} - 28 X^{6} + 322 X^{5} - 1960 X^{4} + 6769 X^{3} - 13132 X^{2} + 13068 X - 5040

= (X^{7} - 28 X^{6} + 322 X^{5} - 1960 X^{4} + 6769 X^{3} - 13132 X^{2} + 13068 X - 5040) (X - 8) (X - 9) (X - 10) (X - 11)

(X^{7} - 28 X^{6} + 322 X^{5} - 1960 X^{4} + 6769 X^{3} - 13132 X^{2} + 13068 X - 5040) (X - 8)

확대한다:

X^{8} - 36 X^{7} + 546 X^{6} - 4536 X^{5} + 22449 X^{4} - 67284 X^{3} + 118124 X^{2} - 109584 X + 40320

= (X^{8} - 36 X^{7} + 546 X^{6} - 4536 X^{5} + 22449 X^{4} - 67284 X^{3} + 118124 X^{2} - 109584 X + 40320) (X - 9) (X - 10) (X - 11)

(X^{8} - 36 X^{7} + 546 X^{6} - 4536 X^{5} + 22449 X^{4} - 67284 X^{3} + 118124 X^{2} - 109584 X + 40320) (X - 9)

확대한다:

X^{9} - 45 X^{8} + 870 X^{7} - 9450 X^{6} + 63273 X^{5} - 269325 X^{4} + 723680 X^{3} - 1172700 X^{2} + 1026576 X - 362880

= (X^{9} - 45 X^{8} + 870 X^{7} - 9450 X^{6} + 63273 X^{5} - 269325 X^{4} + 723680 X^{3} - 1172700 X^{2} + 1026576 X - 362880) (X - 10) (X - 11)

(X^{9} - 45 X^{8} + 870 X^{7} - 9450 X^{6} + 63273 X^{5} - 269325 X^{4} + 723680 X^{3} - 1172700 X^{2} + 1026576 X - 362880) (X - 10)

확대한다:

X^{10} - 55 X^{9} + 1320 X^{8} - 18150 X^{7} + 157773 X^{6} - 902055 X^{5} + 3416930 X^{4} - 8409500 X^{3} + 12753576 X^{2} - 10628640 X + 3628800

= (X^{10} - 55 X^{9} + 1320 X^{8} - 18150 X^{7} + 157773 X^{6} - 902055 X^{5} + 3416930 X^{4} - 8409500 X^{3} + 12753576 X^{2} - 10628640 X + 3628800) (X - 11)

(X^{10} - 55 X^{9} + 1320 X^{8} - 18150 X^{7} + 157773 X^{6} - 902055 X^{5} + 3416930 X^{4} - 8409500 X^{3} + 12753576 X^{2} - 10628640 X + 3628800) (X - 11)

확대한다:

X^{11} - 66 X^{10} + 1925 X^{9} - 32670 X^{8} + 357423 X^{7} - 2637558 X^{6} + 13339535 X^{5} - 45995730 X^{4} + 105258076 X^{3} - 150917976 X^{2} + 120543840 X - 39916800

= X^{11} - 66 X^{10} + 1925 X^{9} - 32670 X^{8} + 357423 X^{7} - 2637558 X^{6} + 13339535 X^{5} - 45995730 X^{4} + 105258076 X^{3} - 150917976 X^{2} + 120543840 X - 39916800

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