忙しい人のための中学数学【因数分解の解答／中編】

　因数分解の問題の解答編です。一通り解答まとめました。今後もう少し細かい途中式も追加するかも？（解説用に）

　こちらが問題編のnoteです。

　その他の単元や計算問題は、こちらのリンク集からどうぞ↓

乗法の公式①【その1】・・・計60問

A（20問）

① x²+3x+2
=(x+1)(x+2)

② x²+5x+6
=(x+2)(x+3)

③ x²+7x+12
=(x+3)(x+4)

④ x²+9x+20
=(x+4)(x+5)

⑤ x²+11x+30
=(x+5)(x+6)

⑥ x²+13x+42
=(x+6)(x+7)

⑦ x²+15x+56
=(x+7)(x+8)

⑧ x²+17x+72
=(x+8)(x+9)

⑨ x²+19x+90
=(x+9)(x+10)

⑩ x²+4x+3
=(x+1)(x+3)

⑪ x²+6x+8
=(x+2)(x+4)

⑫ x²+8x+15
=(x+3)(x+5)

⑬ x²+10x+24
=(x+4)(x+6)

⑭ x²+12x+35
=(x+5)(x+7)

⑮ x²+14x+48
=(x+6)(x+8)

⑯ x²+16x+63
=(x+7)(x+9)

⑰ x²+18x+80
=(x+8)(x+10)

⑱ x²+20x+99
=(x+9)(x+11)

⑲ x²+5x+4
=(x+1)(x+4)

⑳ x²+7x+10
=(x+2)(x+5)

B（20問）

① x²+9x+18
=(x+3)(x+6)

② x²+11x+28
=(x+4)(x+7)

③ x²+13x+40
=(x+5)(x+8)

④ x²+15x+54
=(x+6)(x+9)

⑤ x²+17x+70
=(x+7)(x+10)

⑥ x²+19x+88
=(x+8)(x+11)

⑦ x²+21x+108
=(x+9)(x+12)

⑧ x²+6x+5
=(x+1)(x+5)

⑨ x²+8x+12
=(x+2)(x+6)

⑩ x²+10x+21
=(x+3)(x+7)

⑪ x²+12x+32
=(x+4)(x+8)

⑫ x²+14x+45
=(x+5)(x+9)

⑬ x²+16x+60
=(x+6)(x+10)

⑭ x²+18x+77
=(x+7)(x+11)

⑮ x²+20x+96
=(x+8)(x+12)

⑯ x²+22x+117
=(x+9)(x+13)

⑰ x²+7x+6
=(x+1)(x+6)

⑱ x²+9x+14
=(x+2)(x+7)

⑲ x²+11x+24
=(x+3)(x+8)

⑳ x²+13x+36
=(x+4)(x+9)

C（20問）

① x²+15x+50
=(x+5)(x+10)

② x²+17x+66
=(x+6)(x+11)

③ x²+19x+84
=(x+7)(x+12)

④ x²+21x+104
=(x+8)(x+13)

⑤ x²+23x+126
=(x+9)(x+14)

⑥ x²+8x+7
=(x+1)(x+7)

⑦ x²+10x+16
=(x+2)(x+8)

⑧ x²+12x+27
=(x+3)(x+9)

⑨ x²+14x+40
=(x+4)(x+10)

⑩ x²+16x+55
=(x+5)(x+11)

⑪ x²+18x+72
=(x+6)(x+12)

⑫ x²+20x+91
=(x+7)(x+13)

⑬ x²+22x+112
=(x+8)(x+14)

⑭ x²+24x+135
=(x+9)(x+15)

⑮ x²+9x+8
=(x+1)(x+8)

⑯ x²+11x+18
=(x+2)(x+9)

⑰ x²+13x+30
=(x+3)(x+10)

⑱ x²+15x+44
=(x+4)(x+11)

⑲ x²+17x+60
=(x+5)(x+12)

⑳ x²+19x+78
=(x+6)(x+13)

乗法の公式①【その2】・・・計60問

A（20問）

① x²−3x+2
=(x−1)(x−2)

② x²−5x+6
=(x−2)(x−3)

③ x²−7x+12
=(x−3)(x−4)

④ x²−9x+20
=(x−4)(x−5)

⑤ x²−11x+30
=(x−5)(x−6)

⑥ x²−13x+42
=(x−6)(x−7)

⑦ x²−15x+56
=(x−7)(x−8)

⑧ x²−17x+72
=(x−8)(x−9)

⑨ x²−19x+90
=(x−9)(x−10)

⑩ x²−4x+3
=(x−1)(x−3)

⑪ x²−6x+8
=(x−2)(x−4)

⑫ x²−8x+15
=(x−3)(x−5)

⑬ x²−10x+24
=(x−4)(x−6)

⑭ x²−12x+35
=(x−5)(x−7)

⑮ x²−14x+42
=(x−6)(x−8)

⑯ x²−16x+63
=(x−7)(x−9)

⑰ x²−18x+80
=(x−8)(x−10)

⑱ x²−20x+99
=(x−9)(x−11)

⑲ x²−5x+4
=(x−1)(x−4)

⑳ x²−7x+10
=(x−2)(x−5)

B（20問）

① x²−9x+18
=(x−3)(x−6)

② x²−11x+28
=(x−4)(x−7)

③ x²−13x+40
=(x−5)(x−8)

④ x²−15x+54
=(x−6)(x−9)

⑤ x²−17x+70
=(x−7)(x−10)

⑥ x²−19x+88
=(x−8)(x−11)

⑦ x²−21x+108
=(x−9)(x−12)

⑧ x²−6x+5
=(x−1)(x−5)

⑨ x²−8x+12
=(x−2)(x−6)

⑩ x²−10x+21
=(x−3)(x−7)

⑪ x²−12x+32
=(x−4)(x−8)

⑫ x²−14x+45
=(x−5)(x−9)

⑬ x²−16x+60
=(x−6)(x−10)

⑭ x²−18x+77
=(x−7)(x−11)

⑮ x²−20x+96
=(x−8)(x−12)

⑯ x²−22x+117
=(x−9)(x−13)

⑰ x²−7x+6
=(x−1)(x−6)

⑱ x²−9x+14
=(x−2)(x−7)

⑲ x²−11x+24
=(x−3)(x−8)

⑳ x²−13x+36
=(x−4)(x−9)

C（20問）

① x²−15x+50
=(x−5)(x−10)

② x²−17x+66
=(x−6)(x−11)

③ x²−19x+84
=(x−7)(x−12)

④ x²−21x+104
=(x−8)(x−13)

⑤ x²−23x+126
=(x−9)(x−14)

⑥ x²−8x+7
=(x−1)(x−7)

⑦ x²−10x+16
=(x−2)(x−8)

⑧ x²−12x+27
=(x−3)(x−9)

⑨ x²−14x+40
=(x−4)(x−10)

⑩ x²−16x+55
=(x−5)(x−11)

⑪ x²−18x+72
=(x−6)(x−12)

⑫ x²−20x+91
=(x−7)(x−13)

⑬ x²−22x+112
=(x−8)(x−14)

⑭ x²−24x+135
=(x−9)(x−15)

⑮ x²−9x+8
=(x−1)(x−8)

⑯ x²−11x+18
=(x−2)(x−9)

⑰ x²−13x+30
=(x−3)(x−10)

⑱ x²−15x+44
=(x−4)(x−11)

⑲ x²−17x+60
=(x−5)(x−12)

⑳ x²−19x+78
=(x−6)(x−13)

乗法の公式①【その3】・・・計60問

A（20問）

① x²−x−2
=(x+1)(x−2)

② x²−x−6
=(x+2)(x−3)

③ x²−x−12
=(x+3)(x−4)

④ x²−x−20
=(x+4)(x−5)

⑤ x²−x−30
=(x+5)(x−6)

⑥ x²−x−42
=(x+6)(x−7)

⑦ x²−x−56
=(x+7)(x−8)

⑧ x²−x−72
=(x+8)(x−9)

⑨ x²−x−90
=(x+9)(x−10)

⑩ x²−2x−3
=(x+1)(x−3)

⑪ x²−2x−8
=(x+2)(x−4)

⑫ x²−2x−15
=(x+3)(x−5)

⑬ x²−2x−24
=(x+4)(x−6)

⑭ x²−2x−35
=(x+5)(x−7)

⑮ x²−2x−48
=(x+6)(x−8)

⑯ x²−2x−63
=(x+7)(x−9)

⑰ x²−2x−80
=(x+8)(x−10)

⑱ x²−2x−99
=(x+9)(x−11)

⑲ x²−3x−4
=(x+1)(x−4)

⑳ x²−3x−10
=(x+2)(x−5)

B（20問）

① x²−3x−18
=(x+3)(x−6)

② x²−3x−28
=(x+4)(x−7)

③ x²−3x−40
=(x+5)(x−8)

④ x²−3x−54
=(x+6)(x−9)

⑤ x²−3x−70
=(x+7)(x−10)

⑥ x²−3x−88
=(x+8)(x−11)

⑦ x²−3x−108
=(x+9)(x−12)

⑧ x²−4x−5
=(x+1)(x−5)

⑨ x²−4x−12
=(x+2)(x−6)

⑩ x²−4x−21
=(x+3)(x−7)

⑪ x²−4x−32
=(x+4)(x−8)

⑫ x²−4x−45
=(x+5)(x−9)

⑬ x²−4x−60
=(x+6)(x−10)

⑭ x²−4x−77
=(x+7)(x−11)

⑮ x²−4x−96
=(x+8)(x−12)

⑯ x²−4x−117
=(x+9)(x−13)

⑰ x²−5x−6
=(x+1)(x−6)

⑱ x²−5x−14
=(x+2)(x−7)

⑲ x²−5x−24
=(x+3)(x−8)

⑳ x²−5x−36
=(x+4)(x−9)

C（20問）

① x²−5x−50
=(x+5)(x−10)

② x²−5x−66
=(x+6)(x−11)

③ x²−5x−84
=(x+7)(x−12)

④ x²−5x−104
=(x+8)(x−13)

⑤ x²−5x−126
=(x+9)(x−14)

⑥ x²−6x−7
=(x+1)(x−7)

⑦ x²−6x−16
=(x+2)(x−8)

⑧ x²−6x−27
=(x+3)(x−9)

⑨ x²−6x−40
=(x+4)(x−10)

⑩ x²−6x−55
=(x+5)(x−11)

⑪ x²−6x−72
=(x+6)(x−12)

⑫ x²−6x−91
=(x+7)(x−13)

⑬ x²−6x−112
=(x+8)(x−14)

⑭ x²−6x−135
=(x+9)(x−15)

⑮ x²−7x−8
=(x+1)(x−8)

⑯ x²−7x−18
=(x+2)(x−9)

⑰ x²−7x−30
=(x+3)(x−10)

⑱ x²−7x−44
=(x+4)(x−11)

⑲ x²−7x−60
=(x+5)(x−12)

⑳ x²−7x−78
=(x+6)(x−13)

乗法の公式①【その4】・・・計60問

A（20問）

① x²+x−2
=(x−1)(x+2)

② x²+x−6
=(x−2)(x+3)

③ x²+x−12
=(x−3)(x+4)

④ x²+x−20
=(x−4)(x+5)

⑤ x²+x−30
=(x−5)(x+6)

⑥ x²+x−42
=(x−6)(x+7)

⑦ x²+x−56
=(x−7)(x+8)

⑧ x²+x−72
=(x−8)(x+9)

⑨ x²+x−90
=(x−9)(x+10)

⑩ x²+2x−3
=(x−1)(x+3)

⑪ x²+2x−8
=(x−2)(x+4)

⑫ x²+2x−15
=(x−3)(x+5)

⑬ x²+2x−24
=(x−4)(x+6)

⑭ x²+2x−35
=(x−5)(x+7)

⑮ x²+2x−48
=(x−6)(x+8)

⑯ x²+2x−63
=(x−7)(x+9)

⑰ x²+2x−80
=(x−8)(x+10)

⑱ x²+2x−99
=(x−9)(x+11)

⑲ x²+3x−4
=(x−1)(x+4)

⑳ x²+3x−10
=(x−2)(x+5)

B（20問）

① x²+3x−18
=(x−3)(x+6)

② x²+3x−28
=(x−4)(x+7)

③ x²+3x−40
=(x−5)(x+8)

④ x²+3x−54
=(x−6)(x+9)

⑤ x²+3x−70
=(x−7)(x+10)

⑥ x²+3x−88
=(x−8)(x+11)

⑦ x²+3x−108
=(x−9)(x+12)

⑧ x²+4x−5
=(x−1)(x+5)

⑨ x²+4x−12
=(x−2)(x+6)

⑩ x²+4x−21
=(x−3)(x+7)

⑪ x²+4x−32
=(x−4)(x+8)

⑫ x²+4x−45
=(x−5)(x+9)

⑬ x²+4x−60
=(x−6)(x+10)

⑭ x²+4x−77
=(x−7)(x+11)

⑮ x²+4x−96
=(x−8)(x+12)

⑯ x²+4x−117
=(x−9)(x+13)

⑰ x²+5x−6
=(x−1)(x+6)

⑱ x²+5x−14
=(x−2)(x+7)

⑲ x²+5x−24
=(x−3)(x+8)

⑳ x²+5x−36
=(x−4)(x+9)

C（20問）

① x²+5x−50
=(x−5)(x+10)

② x²+5x−66
=(x−6)(x+11)

③ x²+5x−84
=(x−7)(x+12)

④ x²+5x−104
=(x−8)(x+13)

⑤ x²+5x−126
=(x−9)(x+14)

⑥ x²+6x−7
=(x−1)(x+7)

⑦ x²+6x−16
=(x−2)(x+8)

⑧ x²+6x−27
=(x−3)(x+9)

⑨ x²+6x−40
=(x−4)(x+10)

⑩ x²+6x−55
=(x−5)(x+11)

⑪ x²+6x−72
=(x−6)(x+12)

⑫ x²+6x−91
=(x−7)(x+13)

⑬ x²+6x−112
=(x−8)(x+14)

⑭ x²+6x−135
=(x−9)(x+15)

⑮ x²+7x−8
=(x−1)(x+8)

⑯ x²+7x−18
=(x−2)(x+9)

⑰ x²+7x−30
=(x−3)(x+10)

⑱ x²+7x−44
=(x−4)(x+11)

⑲ x²+7x−60
=(x−5)(x+12)

⑳ x²+7x−78
=(x−6)(x+13)

乗法の公式②・・・計40問

A（20問）

① x²+2x+1
=(x+1)²

② x²+4x+4
=(x+2)²

③ x²+6x+9
=(x+3)²

④ x²+8x+16
=(x+4)²

⑤ x²+10x+25
=(x+5)²

⑥ x²+12x+36
=(x+6)²

⑦ x²+14x+49
=(x+7)²

⑧ x²+16x+64
=(x+8)²

⑨ x²+18x+81
=(x+9)²

⑩ x²+20x+100
=(x+10)²

⑪ x²+22x+121
=(x+11)²

⑫ x²+24x+144
=(x+12)²

⑬ x²+26x+169
=(x+13)²

⑭ x²+28x+196
=(x+14)²

⑮ x²+30x+225
=(x+15)²

⑯ 4x²+4xy+y²
=(2x+y)²

⑰ 9x²+12xy+4y²
=(3x+2y)²

⑱ 16x²+24xy+9y²
=(4x+3y)²

⑲ 25x²+40xy+16y²
=(5x+4y)²

⑳ 36x²+60xy+25y²
=(6x+5y)²

B（20問）

① 49x²+84xy+36y²
=(7x+6y)²

② 64x²+112xy+49y²
=(8x+7y)²

③ 81x²+144xy+64y²
=(9x+8y)²

④ 100x²+180xy+81y²
=(10x+9y)²

⑤ 121x²+220xy+100y²
=(11x+10y)²

⑥ 144x²+264xy+121y²
=(12x+11y)²

⑦ 169x²+312xy+144y²
=(13x+12y)²

⑧ 196x²+364xy+169y²
=(14x+13y)²

⑨ 225x²+420xy+196y²
=(15x+14y)²

⑩ x²+4xy+4y²
=(x+2y)²

⑪ 4x²+12xy+9y²
=(2x+3y)²

⑫ 9x²+24xy+16y²
=(3x+4y)²

⑬ 16x²+40xy+25y²
=(4x+5y)²

⑭ 25x²+60xy+36y²
=(5x+6y)²

⑮ 36x²+84xy+49y²
=(6x+7y)²

⑯ 49x²+112xy+64y²
=(7x+8y)²

⑰ 64x²+144xy+81y²
=(8x+9y)²

⑱ 81x²+180xy+100y²
=(9x+10y)²

⑲ 100x²+220xy+121y²
=(10x+11y)²

⑳ 121x²+264xy+144y²
=(11x+12y)²

乗法の公式③・・・計40問

A（20問）

① x²−2x+1
=(x−1)²

② x²−4x+4
=(x−2)²

③ x²−6x+9
=(x−3)²

④ x²−8x+16
=(x−4)²

⑤ x²−10x+25
=(x−5)²

⑥ x²−12x+36
=(x−6)²

⑦ x²−14x+49
=(x−7)²

⑧ x²−16x+64
=(x−8)²

⑨ x²−18x+81
=(x−9)²

⑩ x²−20x+100
=(x−10)²

⑪ x²−22x+121
=(x−11)²

⑫ x²−24x+144
=(x−12)²

⑬ x²−26x+169
=(x−13)²

⑭ x²−28x+196
=(x−14)²

⑮ x²−30x+225
=(x−15)²

⑯ 4x²−4xy+y²
=(2x−y)²

⑰ 9x²−12xy+4y²
=(3x−2y)²

⑱ 16x²−24xy+9y²
=(4x−3y)²

⑲ 25x²−40xy+16y²
=(5x−4y)²

⑳ 36x²−60xy+25y²
=(6x−5y)²

B（20問）

① 49x²−84xy+36y²
=(7x−6y)²

② 64x²−112xy+49y²
=(8x−7y)²

③ 81x²−144xy+64y²
=(9x−8y)²

④ 100x²−180xy+81y²
=(10x−9y)²

⑤ 121x²−220xy+100y²
=(11x−10y)²

⑥ 144x²−264xy+121y²
=(12x−11y)²

⑦ 169x²−312xy+144y²
=(13x−12y)²

⑧ 196x²−364xy+169y²
=(14x−13y)²

⑨ 225x²−420xy+196y²
=(15x−14y)²

⑩ x²−4xy+4y²
=(x−2y)²

⑪ 4x²−12xy+9y²
=(2x−3y)²

⑫ 9x²−24xy+16y²
=(3x−4y)²

⑬ 16x²−40xy+25y²
=(4x−5y)²

⑭ 25x²−60xy+36y²
=(5x−6y)²

⑮ 36x²−84xy+49y²
=(6x−7y)²

⑯ 49x²−112xy+64y²
=(7x−8y)²

⑰ 64x²−144xy+81y²
=(8x−9y)²

⑱ 81x²−180xy+100y²
=(9x−10y)²

⑲ 100x²−220xy+121y²
=(10x−11y)²

⑳ 121x²−264xy+144y²
=(11x−12y)²

乗法の公式④・・・計40問

A（20問）

① x²−1
=(x+1)(x−1)

② x²−4
=(x+2)(x−2)

③ x²−9
=(x+3)(x−3)

④ x²−16
=(x+4)(x−4)

⑤ x²−25
=(x+5)(x−5)

⑥ x²−36
=(x+6)(x−6)

⑦ x²−49
=(x+7)(x−7)

⑧ x²−64
=(x+8)(x−8)

⑨ x²−81
=(x+9)(x−9)

⑩ x²−100
=(x+10)(x−10)

⑪ x²−121
=(x+11)(x−11)

⑫ x²−144
=(x+12)(x−12)

⑬ x²−169
=(x+13)(x−13)

⑭ x²−196
=(x+14)(x−14)

⑮ x²−225
=(x+15)(x−15)

⑯ 4x²−y²
=(2x+y)(2x−y)

⑰ 9x²−4y²
=(3x+2y)(3x−2y)

⑱ 16x²−9y²
=(4x+3y)(4x−3y)

⑲ 25x²−16y²
=(5x+4y)(5x−4y)

⑳ 36x²−25y²
=(6x+5y)(6x−5y)

B（20問）

① 49x²−36y²
=(7x+6y)(7x−6y)

② 64x²−49y²
=(8x+7y)(8x−7y)

③ 81x²−64y²
=(9x+8y)(9x−8y)

④ 100x²−81y²
=(10x+9y)(10x−9y)

⑤ 121x²−100y²
=(11x+10y)(11x−10y)

⑥ 144x²−121y²
=(12x+11y)(12x−11y)

⑦ 169x²−144y²
=(13x+12y)(13x−12y)

⑧ 196x²−169y²
=(14x+13y)(14x−13y)

⑨ 225x²−196y²
=(15x+14y)(15x−14y)

⑩ a²−b²
=(a+b)(a−b)

⑪ a²−9b²
=(a+3b)(a−3b)

⑫ a²−25b²
=(a+5b)(a−5b)

⑬ a²−49b²
=(a+7b)(a−7b)

⑭ a²−81b²
=(a+9b)(a−9b)

⑮ 4−t²
=(2+t)(2−t)

⑯ 16−9t²
=(4+3t)(4−3t)

⑰ 36−25t²
=(6+5t)(6−5t)

⑱ 64−49t²
=(8+7t)(8−7t)

⑲ 100−81t²
=(10+9t)(10−9t)

⑳ 144−121t²
=(12+11t)(12−11t)