数学Ⅰ やや複雑な因数分解 No．3

数学Ⅰ やや複雑な因数分解Ｎｏ．３
１Ｓｔｅｐ３
(5) 6x 2 -13xy +6y 2-5x +5y +1 (9) 6x 2 +7xy-3y 2 +x -4y -1
次の式を因数分解せよ。
(1) x - xy -6y +2x -y +1 2
2
(10) 6x 2 +4xy-2y 2 -5x - y +1 (2) x -2xy +y + x -y -2 2
2
(6) x 2+4xy +3y 2 +2y -1 (7) 3x 2 +2xy- y 2 -3x +5y -6 (3) 2x 2 -4xy-6y 2 -x +11y -3
(4) 3x 2 -5xy+2y 2 +x -2y -4
(8) 6x 2 -7xy+2y 2 -6x +5y -12 (11) 6x 2 -5xy+ y 2 +5x -3y -4
(12) 12x 2 -7xy + y 2 -x -1
数学Ⅰ やや複雑な因数分解Ｎｏ．３
１Ｓｔｅｐ３
(5) 6x 2 -13xy +6y 2-5x +5y +1 No.２２ (5) と同じ問題
(9) 6x 2 +7xy-3y 2 +x -4y -1
次の式を因数分解せよ。
=6x 2 - 0 13y +5 1x +6y 2 +5y +1 2 1 . 3
=6x 2 + 0 7y +11x -3y 2 -4y -1 1 1 . 3
(1) x 2- xy -6y 2 +2x -y +1 No.２２ (1) と同じ問題
=6x 2 - 0 13y +5 1x + 0 2y +1 10 3y +1 1 3 1 . 2
=6x 2 + 0 7y +11x - 0 3y 2 +4y +11 3 1 . 1
= x 2 - 0 y -2 1x -6y 2 - y +1 2 1 . 3
2 -0 3y + 1 1 . -9y -3 =6x 2 + 0 7y +11x - 0 y +1 10 3y +11 4
= x 2 - 0 y -2 1x -0 6y 2 + y -11 3 -1 . -2
3 -0 2y + 1 1 . -4y -2
5
= x - 0 y -2 1x -0 2y +1 10 3y -1 1 1
1 -0 3y - 1 1 . -3y +1
-13y -5
2 3y +1 . 9y +3
3 -0 y + 1 1 . -2y -2
より， 6 2x - 0 3y +11 76 3x -0 2y +1 1 7
7y +1
1 2y +1 . 2y +1
-y +2
=0 2x -3y -1 10 3x -2y -1 1
より， 0 2x +3y +116 3x - 0 y +11 7
2
= 0 2x +3y +1 10 3x - y -1 1
より， 6 x - 0 3y -1 1 70 x +2y +1 1 = 0 x -3y +110 x +2y +11
(10) 6x 2 +4xy-2y 2 -5x - y +1 No.２２ (4) と同じ問題
(2) x -2xy +y + x -y -2 No.１２ (2) と同じ問題
2
2
= x 2 - 0 2y -1 1x +y 2 - y -2
= x 2 - 0 2y -1 1x +0 y -2 10 y +1 1
1 -0 y - 2 1 . -y +2
1 -0 y + 1 1 . -y -1
-2y +1
(6) x 2+4xy +3y 2 +2y -1 3 -1 . -1
= x 2 +4xy+ 0 3y -1 10 y +1 1 1 1 . 3
1 3y -1 . 3y -1 2
1 y +1 . y +1
4y
より， 0 x +3y -1 10 x + y +1 1
より， 6 x - 0 y -2 1 76 x - 0 y +1 1 7 =0 x - y +2 10 x -y -1 1
(3) 2x 2 -4xy-6y 2 -x +11y -3
=2x 2 - 0 4y +11x -6y 2 +11y -3 3 -1 . -2
=2x 2 - 0 4y +11x - 0 6y 2 -11y +31 2 -3 . -9
=2x 2 - 0 4y +11x - 0 3y -110 2y -3 1 -11
2 2y -3 . 2y -3
1 -0 3y - 1 1 . -6y +2
-4y -1
より， 0 2x +2y -316 x - 0 3y -11 7
=6x 2 + 0 4y -5 1x -2y 2 - y +1 2 -1 . -1
=6x 2 + 0 4y -51x - 0 2y 2 +y -11 1 1 . 2
=6x 2 + 0 4y -51x - 0 2y -110 y +11 1
3 -0 y + 1 1 . -2y -2
2 2y -1 . 6y -3
4y -5
より， 6 3x - 0 y +1 1 70 2x +2y -11
(7) 3x 2 +2xy- y 2 -3x +5y -6 No.２２ (3) と同じ問題
=3x 2 + 0 2y -31x - y 2 +5y -6
=3x 2 + 0 2y -31x - 0 y 2 -5y +61
=3x 2 + 0 2y -31x - 0 y -2 10 y -3 1
1 y -2 . 3y -6
3 -0 y -3 1 . -y +3
2y -3
より， 0 x+ y -2 16 3x - 0 y -3 1 7
=0 x+y -210 3x -y +31
= 0 3x - y -110 2x +2y -1 1
(11) 6x 2 -5xy+ y 2 +5x -3y -4
=6x 2 - 0 5y -51x + y 2 -3y -4
=6x 2 - 0 5y -51x + 0 y -4 10 y +1 1
3 -0 y -4 1 . -2y +8
2 -0 y +1 1 . -3y -3
-5y +5
より， 6 3x - 0 y -4 1 76 2x - 0 y +1 1 7
=0 3x -y +410 2x -y -11
=0 2x +2y -3 10 x -3y +1 1
(4) 3x 2 -5xy+2y 2 +x -2y -4
=3x 2 - 0 5y -11x +2y 2 -2y -4
=3x 2 - 0 5y -11x +20 y 2 - y -21
2
=3x - 0 5y -11x +20 y -210 y +11
3 -20 y - 2 1 . -2y +4
. -3y -3
-5y +1
1 -0 y + 1 1
より， 6 3x -20 y -21 76 x - 0 y +1 1 7
=0 3x -2y +4 10 x -y -11
(8) 6x 2 -7xy+2y 2 -6x +5y -12 No.１２ (5) と同じ問題
=6x 2 - 0 7y +61x +2y 2 +5y -12 2 -3 . -3
=6x 2 - 0 7y +61x + 0 2y -310 y +41 1 4 . 8
2 -0 y +4 1 . -3y -12 5
3 -0 2y - 3 1 . -4y +6
-7y -6
より， 6 2x - 0 y +4 1 76 3x - 0 2y -31 7
=0 2x -y -410 3x -2y +3 1
(12) 12x 2 -7xy + y 2 -x -1
=12x 2 - 0 7y +1 1x + y 2 -1
=12x 2 - 0 7y +1 1x + 0 y -110 y +11
3 -0 y + 1 1 . -4y -4
4 -0 y - 1 1 . -3y +3
-7y -1
より， 6 3x - 0 y +1 1 76 4x - 0 y -1 1 7
=0 3x -y -110 4x -y +11

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