【中学3年数学】1-2 因数分解｜問題集
1.次の式を因数分解しなさい。
(1)\(xy+ay\)
\(=y(x+a)\)
(2)\(ax-3x\)
\(=x(a-3)\)
(3)\(x^2-x\)
\(=x(x-1)\)
(4)\(5a^2-10a\)
\(=5a(a-2)\)
(5)\(6ax-3ax^2\)
\(=3ax(2-x)\)
(6)\(mx+my-mz\)
\(=m(x+y-z)\)
(7)\(x^2+8x+12\)
\(=(x+2)(x+6)\)
(8)\(x^2-9x+20\)
\(=(x-4)(x-5)\)
(9)\(x^2+6x+8\)
\(=(x+2)(x+4)\)
(10)\(x^2+7x+6\)
\(=(x+1)(x+6)\)
(11)\(x^2+10x+24\)
\(=(x+4)(x+6)\)
(12)\(x^2-4x+3\)
\(=(x-1)(x-3)\)
(13)\(x^2-12x+35\)
\(=(x-5)(x-7)\)
(14)\(x^2-9x+14\)
\(=(x-2)(x-7)\)
(15)\(x^2+x-12\)
\(=(x+4)(x-3)\)
(16)\(x^2-7x-18\)
\(=(x+2)(x-9)\)
(17)\(x^2-x-6\)
\(=(x+2)(x-3)\)
(18)\(x^2+6x-16\)
\(=(x+8)(x-2)\)
(19)\(x^2+5x-24\)
\(=(x+8)(x-3)\)
(20)\(x^2-3x-28\)
\(=(x+4)(x-7)\)
(21)\(x^2+2x-63\)
\(=(x+9)(x-7)\)
(22)\(x^2-4x-60\)
\(=(x+6)(x-10)\)
(23)\(x^2+6x+9\)
\(=(x+3)^2\)
(24)\(a^2-4a+4\)
\(=(a-2)^2\)
(25)\(x^2+14x+49\)
\(=(x+7)^2\)
(26)\(x^2-16x+64\)
\(=(x-8)^2\)
(27)\(4x^2+20x+25\)
\(=(2x+5)^2\)
(28)\(16x^2-24xy+9y^2\)
\(=(4x-3y)^2\)
(29)\(x^2-49\)
\(=(x+7)(x-7)\)
(30)\(x^2-9\)
\(=(x+3)(x-3)\)
(31)\(a^2-1\)
\(=(a+1)(a-1)\)
(32)\(9x^2-16\)
\(=(3x+4)(3x-4)\)
(33)\(49x^2-4\)
\(=(7x+2)(7x-2)\)
(34)\(16x^2-25y^2\)
\(=(4x+5y)(4x-5y)\)
(35)\(x^2+10x+25\)
\(=(x+5)^2\)
(36)\(x^2-5x-36\)
\(=(x+4)(x-9)\)
(37)\(x^2+5x\)
\(=x(x+5)\)
(38)\(3ax-9bx\)
\(=3x(a-3b)\)
(39)\(x^2+9x+18\)
\(=(x+3)(x+6)\)
(40)\(x^2-10x+25\)
\(=(x-5)^2\)
(41)\(x^2-x-30\)
\(=(x+5)(x-6)\)
(42)\(x^2-64\)
\(=(x+8)(x-8)\)
(43)\(x^2-7x+12\)
\(=(x-3)(x-4)\)
(44)\(x^2+14x+24\)
\(=(x+2)(x+12)\)
(45)\(x^2+4x-5\)
\(=(x-1)(x+5)\)
(46)\(x^2+26x+169\)
\(=(x+13)^2\)
(47)\(\displaystyle a^2-\frac{4}{9}\)
\(\displaystyle =\left(a+\frac{2}{3}\right)\left(a-\frac{2}{3}\right)\)
(48)\(x^2-12xy+20y^2\)
\(=(x-2y)(x-10y)\)
(49)\(x^2+24xy+144y^2\)
\(=(x+12y)^2\)
(50)\(x^2-xy-56y^2\)
\(=(x+7y)(x-8y)\)
(51)\(25x^2-81\)
\(=(5x+9)(5x-9)\)
(52)\(9x^2+12x+4\)
\(=(3x+2)^2\)
(53)\(16x^2+40x+25\)
\(=(4x+5)^2\)
(54)\(4x^2-12xy+9y^2\)
\(=(2x-3y)^2\)
(55)\(100x^2-1\)
\(=(10x+1)(10x-1)\)
(56)\(64a^2-9b^2\)
\(=(8a+3b)(8a-3b)\)
(57)\(3x^2+9x\)
\(=3x(x+3)\)
(58)\(x^2+13x+36\)
\(=(x+4)(x+9)\)
(59)\(x^2+3x-10\)
\(=(x+5)(x-2)\)
(60)\(x^2-4\)
\(=(x+2)(x-2)\)
(61)\(x^2-2x+1\)
\(=(x-1)^2\)
(62)\(25x^2-64y^2\)
\(=(5x+8y)(5x-8y)\)
(63)\(4x^2+28x+49\)
\(=(2x+7)^2\)
(64)\(x^2-11xy+30y^2\)
\(=(x-5y)(x-6y)\)
(65)\(x^2-x-12\)
\(=(x+3)(x-4)\)
(66)\(x^2-6x-7\)
\(=(x+1)(x-7)\)
(67)\(x^2-x-6\)
\(=(x+2)(x-3)\)
(68)\(x^2+12x+36\)
\(=(x+6)^2\)
(69)\(x^2+2x-15\)
\(=(x+5)(x-3)\)
(70)\(x^2-8x+15\)
\(=(x-3)(x-5)\)
(71)\(x^2-169\)
\(=(x+13)(x-13)\)
(72)\(4x^2-4\)
\(=(2x+2)(2x-2)\)
(73)\(x^2+7xy-18y^2\)
\(=(x+9y)(x-2y)\)
(74)\(3x^2-12x-36\)
\(=3(x^2-4x-12)\)
\(=3(x+2)(x-6)\)
\(=3(x+2)(x-6)\)
(75)\(4x^2y-8xy+4y\)
\(=4y(x^2-2x+1)\)
\(=4y(x-1)^2\)
\(=4y(x-1)^2\)
(76)\(x(x-1)+2(x-1)\)
\(=(x+2)(x-1)\)
(77)\((x+3)^2-16\)
\(=(x+3+4)(x+3-4)\)
\(=(x+7)(x-1)\)
\(=(x+7)(x-1)\)
(78)\((x+4)^2+6(x+4)+9\)
\(=(x+4+3)^2\)
\(=(x+7)^2\)
\(=(x+7)^2\)
(79)\((x-2)^2+5(x-2)-36\)
\(=(x-2+9)(x-2-4)\)
\(=(x+7)(x-6)\)
\(=(x+7)(x-6)\)
(80)\(36x^2-24x+4\)
\(=4(9x^2-6x+1)\)
\(=4(3x-1)^2\)
\(=4(3x-1)^2\)
(81)\((x+3)^2-6(x+3)+8\)
\(=(x+3-2)(x+3-4)\)
\(=(x+1)(x-1)\)
\(=(x+1)(x-1)\)
(82)\(a(x-3)-b(x-3)\)
\(=(a-b)(x-3)\)
(83)\((x+1)^2+6(x+1)+8\)
\(=(x+1+2)(x+1+4)\)
\(=(x+3)(x+5)\)
\(=(x+3)(x+5)\)
(84)\((a+b)^2-36\)
\(=(a+b+6)(a+b-6)\)
(85)\((x+y)^2+4(x+y)+4\)
\(=(x+y+2)^2\)
(86)\(2x^2+16x+30\)
\(=2(x^2+8x+15)\)
\(=2(x+3)(x+5)\)
\(=2(x+3)(x+5)\)
(87)\(x^2y-y\)
\(=y(x^2-1)\)
\(=y(x+1)(x-1)\)
\(=y(x+1)(x-1)\)
(88)\(3ax^2+9ax-30a\)
\(=3a(x^2+3x-10)\)
\(=3a(x+5)(x-2)\)
\(=3a(x+5)(x-2)\)
(89)\(4x^2+16xy+16y^2\)
\(=4(x^2+4xy+4y^2)\)
\(=4(x+2y)^2\)
\(=4(x+2y)^2\)
(90)\((x+4)^2-5(x+4)+6\)
\(=(x+4-2)(x+4-3)\)
\(=(x+2)(x+1)\)
\(=(x+2)(x+1)\)
(91)\(5x^2y-25xy-120y\)
\(=5y(x^2-5x-24)\)
\(=5y(x+3)(x-8)\)
\(=5y(x+3)(x-8)\)
(92)\((3x-4)^2-(5x+1)^2\)
\(=\{(3x-4)+(5x+1)\}\{(3x-4)-(5x+1)\}\)
\(=(8x-3)(-2x-5)\)
\(=-(8x-3)(2x+5)\)
\(=(8x-3)(-2x-5)\)
\(=-(8x-3)(2x+5)\)
(93)\((2x+3)(2x-3)+(2x+3)^2\)
\(=(2x+3)(2x-3+2x+3)\)
\(=4x(2x+3)\)
\(=4x(2x+3)\)
(94)\(5x^2-20x+20\)
\(=5(x^2-4x+4)\)
\(=5(x-2)^2\)
\(=5(x-2)^2\)
(95)\((x-1)^2+3(x-1)\)
\(=(x-1)(x-1+3)\)
\(=(x-1)(x+2)\)
\(=(x-1)(x+2)\)
(96)\((x+1)^2-2(x+1)-3\)
\(=(x+1+1)(x+1-3)\)
\(=(x+2)(x-2)\)
\(=(x+2)(x-2)\)
(97)\((x-2)^2-(x-2)-12\)
\(=(x-2+3)(x-2-4)\)
\(=(x+1)(x-6)\)
\(=(x+1)(x-6)\)
(98)\((a+2)^2-9\)
\(=(a+2+3)(a+2-3)\)
\(=(a+5)(a-1)\)
\(=(a+5)(a-1)\)
次の学習に進もう！