{
  "title": "Solving by Factorization (Algebra) - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "Solve by factorization: x² - 5x + 6 = 0 🌱",
      "options": {
        "A": "x = 2, 3",
        "B": "x = -2, -3",
        "C": "x = 1, 6",
        "D": "x = -1, -6"
      },
      "correct_answer": "A"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "Factorize: x² - 9 = 0 🧩",
      "options": {
        "A": "(x+3)(x-3)=0",
        "B": "(x+9)(x-1)=0",
        "C": "(x+3)²=0",
        "D": "(x-3)²=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "Solve: x² - 3x = 0 🌟",
      "options": {
        "A": "x = 0, 3",
        "B": "x = 0, -3",
        "C": "x = 3 only",
        "D": "x = 1, 3"
      },
      "correct_answer": "A"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "Factorize: 2x² - 8 = 0 🔨",
      "options": {
        "A": "2(x-2)(x+2)=0",
        "B": "(2x-4)(x+2)=0",
        "C": "2(x²-4)=0",
        "D": "(x-4)(2x+2)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "Solve: x² + 7x + 12 = 0 🎯",
      "options": {
        "A": "x = -3, -4",
        "B": "x = 3, 4",
        "C": "x = 2, 6",
        "D": "x = -2, -6"
      },
      "correct_answer": "A"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "Factorize: 6x² - 5x - 6 = 0 📊",
      "options": {
        "A": "(2x-3)(3x+2)=0",
        "B": "(3x-2)(2x+3)=0",
        "C": "(6x+1)(x-6)=0",
        "D": "(x-2)(6x+3)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "Solve: x² - 10x + 25 = 0 🎭",
      "options": {
        "A": "x = 5 (double root)",
        "B": "x = -5",
        "C": "x = 5, -5",
        "D": "x = 10, 2.5"
      },
      "correct_answer": "A"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "Factorize: x² - x - 20 = 0 🧠",
      "options": {
        "A": "(x-5)(x+4)=0",
        "B": "(x+5)(x-4)=0",
        "C": "(x-10)(x+2)=0",
        "D": "(x+10)(x-2)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "Solve: 4x² - 9 = 0 🔄",
      "options": {
        "A": "x = ±3/2",
        "B": "x = ±2/3",
        "C": "x = ±9/4",
        "D": "x = ±4/9"
      },
      "correct_answer": "A"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "Factorize: x² + 2x - 15 = 0 ⚖️",
      "options": {
        "A": "(x+5)(x-3)=0",
        "B": "(x-5)(x+3)=0",
        "C": "(x+15)(x-1)=0",
        "D": "(x-15)(x+1)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "Solve: 3x² - 5x - 2 = 0 🎪",
      "options": {
        "A": "x = 2, -1/3",
        "B": "x = -2, 1/3",
        "C": "x = 1, -2/3",
        "D": "x = -1, 2/3"
      },
      "correct_answer": "A"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "Factorize: 9x² - 6x + 1 = 0 🎨",
      "options": {
        "A": "(3x-1)²=0",
        "B": "(9x-1)(x-1)=0",
        "C": "(3x+1)²=0",
        "D": "(x-3)(9x-3)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "Solve: x² - 8x + 16 = 0 🌈",
      "options": {
        "A": "x = 4 (double root)",
        "B": "x = -4",
        "C": "x = 2, 8",
        "D": "x = 4, -4"
      },
      "correct_answer": "A"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "Factorize: 2x² + 7x + 3 = 0 🔵",
      "options": {
        "A": "(2x+1)(x+3)=0",
        "B": "(2x+3)(x+1)=0",
        "C": "(x+3)(2x+1)=0",
        "D": "(x+1)(2x+3)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "Solve: 5x² - 20 = 0 ⚡",
      "options": {
        "A": "x = ±2",
        "B": "x = ±4",
        "C": "x = ±√5",
        "D": "x = ±20"
      },
      "correct_answer": "A"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "Factorize: x² + 9x + 18 = 0 🧨",
      "options": {
        "A": "(x+3)(x+6)=0",
        "B": "(x+2)(x+9)=0",
        "C": "(x+18)(x+1)=0",
        "D": "(x+9)(x+2)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "Solve: 4x² - 12x + 9 = 0 🎡",
      "options": {
        "A": "x = 3/2 (double root)",
        "B": "x = 2/3",
        "C": "x = 3, 1/2",
        "D": "x = -3/2"
      },
      "correct_answer": "A"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Factorize: 3x² - 10x + 3 = 0 🌀",
      "options": {
        "A": "(3x-1)(x-3)=0",
        "B": "(x-1)(3x-3)=0",
        "C": "(3x-3)(x-1)=0",
        "D": "(x-3)(3x-1)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "Solve: x² - 49 = 0 📐",
      "options": {
        "A": "x = ±7",
        "B": "x = ±49",
        "C": "x = 7 only",
        "D": "x = -7 only"
      },
      "correct_answer": "A"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "Factorize: 6x² + 11x - 10 = 0 🍬",
      "options": {
        "A": "(2x+5)(3x-2)=0",
        "B": "(3x+5)(2x-2)=0",
        "C": "(6x-5)(x+2)=0",
        "D": "(x+5)(6x-2)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "Solve by factorization: (x-3)(x+2)=18 🔥",
      "options": {
        "A": "x = 4, -5",
        "B": "x = -4, 5",
        "C": "x = 6, -3",
        "D": "x = 3, -6"
      },
      "correct_answer": "A"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "Factorize: √2x² + 7x + 5√2 = 0 🌐",
      "options": {
        "A": "(√2x+5)(x+√2)=0",
        "B": "(x+5)(√2x+√2)=0",
        "C": "(√2x+√2)(x+5)=0",
        "D": "(2x+5)(x+√2)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "Solve: 1/(x+1) + 2/(x+2) = 4/(x+4), x≠-1,-2,-4 🚀",
      "options": {
        "A": "x = 0, -5/3",
        "B": "x = 0, 5/3",
        "C": "x = 1, -2",
        "D": "No solution"
      },
      "correct_answer": "A"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "Factorize: (x²+1)² - x² = 0 🎲",
      "options": {
        "A": "(x²+x+1)(x²-x+1)=0",
        "B": "(x²+1)²=0",
        "C": "(x²+1-x)(x²+1+x)=0",
        "D": "(x²+1)(x²-1)=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "Solve: (x-1)/(x-2) + (x-3)/(x-4) = 3⅓, x≠2,4 🧿",
      "options": {
        "A": "x = 5/2, 5",
        "B": "x = 2/5, 5",
        "C": "x = 5, 10/3",
        "D": "x = 0, 5"
      },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "Factorize: 12(x²+7x)² - 8(x²+7x)(2x-1) - 15(2x-1)² = 0 ⚙️",
      "options": {
        "A": "[2(x²+7x)-3(2x-1)][6(x²+7x)+5(2x-1)]=0",
        "B": "[3(x²+7x)-5(2x-1)][4(x²+7x)+3(2x-1)]=0",
        "C": "[(x²+7x)-5][12(x²+7x)+3]=0",
        "D": "[(2x-1)-3][4(x²+7x)+5]=0"
      },
      "correct_answer": "A"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "Solve: √(x+1) + √(2x+3) = √(12x+16) 🪐",
      "options": {
        "A": "x = 1",
        "B": "x = 2",
        "C": "x = 3",
        "D": "x = 4"
      },
      "correct_answer": "A"
    },
    
  {
    "id": 28,
    "difficulty": "medium",
    "question": "Factorize: a²b²x² - (a²+b²)x + 1 = 0, a,b≠0 🎯",
    "options": {
      "A": "(abx-1)(abx-1)=0",
      "B": "(a²x-1)(b²x-1)=0",
      "C": "(abx-1)(abx-1)=0",
      "D": "(ax-1)(bx-1)=0"
    },
    "correct_answer": "B"
  },
  {
    "id": 29,
    "difficulty": "medium",
    "question": "Solve: (x²-3x)² - 8(x²-3x) - 20 = 0 🏆",
    "options": {
      "A": "x = 5, -2, 1, 2",
      "B": "x = 1, 2, 5",
      "C": "x = -1, -2, 5",
      "D": "x = 0, 3, 5, -2"
    },
    "correct_answer": "A"
  },
  {
    "id": 30,
    "difficulty": "medium",
    "question": "Factorize: 4√3x² + 5x - 2√3 = 0 🌠",
    "options": {
      "A": "(√3x+2)(4x-√3)=0",
      "B": "(2√3x-1)(2x+2√3)=0",
      "C": "(4x+√3)(√3x-2)=0",
      "D": "(√3x+2)(4x-√3)=0"
    },
    "correct_answer": "A"
  },
  {
    "id": 31,
    "difficulty": "medium",
    "question": "Solve: (2x+3)/(x+1) + (x+1)/(2x+3) = 5/2, x≠-1,-3/2 🎖️",
    "options": {
      "A": "x = 1, -5/3",
      "B": "x = -1, 5/3",
      "C": "x = 0, 1",
      "D": "x = 2, -2/3"
    },
    "correct_answer": "A"
  },
  {
    "id": 32,
    "difficulty": "medium",
    "question": "Factorize: x⁴ - 13x² + 36 = 0 🏔️",
    "options": {
      "A": "(x-2)(x+2)(x-3)(x+3)=0",
      "B": "(x²-4)(x²-9)=0",
      "C": "(x-√2)(x+√2)(x-√3)(x+√3)=0",
      "D": "A and B both"
    },
    "correct_answer": "D"
  },
  {
    "id": 33,
    "difficulty": "medium",
    "question": "Solve: 2(x² - 6) = 3(x - 4) 🌉",
    "options": {
      "A": "x = 3, -4",
      "B": "x = -3, 4",
      "C": "x = 0, 3",
      "D": "x = 0, -4"
    },
    "correct_answer": "A"
  },
  {
    "id": 34,
    "difficulty": "medium",
    "question": "Factorize: 6(x+1/x)² - 25(x+1/x) + 24 = 0, x≠0 🛸",
    "options": {
      "A": "[2(x+1/x)-3][3(x+1/x)-8]=0",
      "B": "[3(x+1/x)-4][2(x+1/x)-6]=0",
      "C": "[6(x+1/x)-8][(x+1/x)-3]=0",
      "D": "[(x+1/x)-2][6(x+1/x)-12]=0"
    },
    "correct_answer": "A"
  },
  {
    "id": 35,
    "difficulty": "medium",
    "question": "Solve: √(3x² - 2) + 1 = 2x 🎇",
    "options": {
      "A": "x = 1",
      "B": "x = 3",
      "C": "x = 1/2",
      "D": "x = √3"
    },
    "correct_answer": "A"
  },
  {
    "id": 36,
    "difficulty": "medium",
    "question": "Factorize: (x²+3x)² - 2(x²+3x) - 8 = 0 🌌",
    "options": {
      "A": "(x²+3x-4)(x²+3x+2)=0",
      "B": "(x²+3x+4)(x²+3x-2)=0",
      "C": "(x²+3x-8)(x²+3x+1)=0",
      "D": "(x²+3x-1)(x²+3x+8)=0"
    },
    "correct_answer": "A"
  },
  {
    "id": 37,
    "difficulty": "medium",
    "question": "Solve: (x-2)/(x-3) + (x-4)/(x-5) = 10/3, x≠3,5 🎡",
    "options": {
      "A": "x = 7/2, 4",
      "B": "x = 4, 5",
      "C": "x = 0, 7/2",
      "D": "x = 3, 5"
    },
    "correct_answer": "A"
  },
  {
    "id": 38,
    "difficulty": "medium",
    "question": "Factorize: 2√2x² + 9x + 5√2 = 0 🔑",
    "options": {
      "A": "(√2x+5)(2x+√2)=0",
      "B": "(2√2x+5)(x+√2)=0",
      "C": "(√2x+1)(2x+5√2)=0",
      "D": "(x+5)(2√2x+√2)=0"
    },
    "correct_answer": "B"
  },
  {
    "id": 39,
    "difficulty": "medium",
    "question": "Solve: |x² - 5x + 6| = x - 2 🎭",
    "options": {
      "A": "x = 2, 4",
      "B": "x = 2 only",
      "C": "x = 4 only",
      "D": "x = 1, 3"
    },
    "correct_answer": "A"
  },
  {
    "id": 40,
    "difficulty": "medium",
    "question": "Factorize: (a+b)²x² - 4abx - (a-b)² = 0 🤖",
    "options": {
      "A": "[(a+b)x-(a-b)][(a+b)x+(a-b)]=0",
      "B": "[(a+b)x-(a-b)]²=0",
      "C": "[x-(a-b)][(a+b)²x+(a-b)]=0",
      "D": "[(a-b)x-(a+b)][(a+b)x+(a-b)]=0"
    },
    "correct_answer": "A"
  },
  {
    "id": 41,
    "difficulty": "hard",
    "question": "Solve: √(x+1) + √(x-1) = 1 🚀",
    "options": {
      "A": "No real solution",
      "B": "x = 1",
      "C": "x = 0",
      "D": "x = 5/4"
    },
    "correct_answer": "A"
  },
  {
    "id": 42,
    "difficulty": "hard",
    "question": "Factorize: x⁶ - 7x³ - 8 = 0 🎲",
    "options": {
      "A": "(x³-8)(x³+1)=0",
      "B": "(x²-2)(x⁴+2x²+4)(x³+1)=0",
      "C": "(x-2)(x²+2x+4)(x+1)(x²-x+1)=0",
      "D": "All of these"
    },
    "correct_answer": "D"
  },
  {
    "id": 43,
    "difficulty": "hard",
    "question": "Solve: (x²+1)² = x²(3x²+1) 🧿",
    "options": {
      "A": "x = ±1",
      "B": "x = ±1/√2",
      "C": "x = ±√2",
      "D": "x = 0, ±1"
    },
    "correct_answer": "A"
  },
  {
    "id": 44,
    "difficulty": "hard",
    "question": "Factorize: (x²+5x+4)(x²+5x+6) - 72 = 0 ⚙️",
    "options": {
      "A": "(x²+5x+12)(x²+5x-2)=0",
      "B": "(x²+5x+10)(x²+5x-8)=0",
      "C": "(x²+5x+8)(x²+5x-6)=0",
      "D": "(x²+5x+9)(x²+5x-4)=0"
    },
    "correct_answer": "A"
  },
  {
    "id": 45,
    "difficulty": "hard",
    "question": "Solve: (x-3)/(x-4) - (x-5)/(x-6) = (x-7)/(x-8) - (x-9)/(x-10), x≠4,6,8,10 🪐",
    "options": {
      "A": "x = 7",
      "B": "x = 5",
      "C": "x = 6",
      "D": "x = 8"
    },
    "correct_answer": "A"
  },
  {
    "id": 46,
    "difficulty": "hard",
    "question": "Factorize: (x²-3x+2)(x²-3x-4) = 144 🎯",
    "options": {
      "A": "(x²-3x-10)(x²-3x+8)=0",
      "B": "(x²-3x-12)(x²-3x+6)=0",
      "C": "(x²-3x-8)(x²-3x+10)=0",
      "D": "(x²-3x-6)(x²-3x+12)=0"
    },
    "correct_answer": "A"
  },
  {
    "id": 47,
    "difficulty": "hard",
    "question": "Solve: √(2x+3) + √(x+1) = √(5x+6) 🏆",
    "options": {
      "A": "x = 2",
      "B": "x = 1",
      "C": "x = 3",
      "D": "x = 0"
    },
    "correct_answer": "A"
  },
  {
    "id": 48,
    "difficulty": "hard",
    "question": "Factorize: 6(2x-3/x)² - 5(2x-3/x) - 25 = 0, x≠0 🌠",
    "options": {
      "A": "[3(2x-3/x)-5][2(2x-3/x)+5]=0",
      "B": "[2(2x-3/x)-5][3(2x-3/x)+5]=0",
      "C": "[6(2x-3/x)-25][(2x-3/x)+1]=0",
      "D": "[(2x-3/x)-5][6(2x-3/x)+5]=0"
    },
    "correct_answer": "B"
  },
  {
    "id": 49,
    "difficulty": "hard",
    "question": "Solve: |x² - 4| = |x-2| 🎖️",
    "options": {
      "A": "x = -2, -1, 2, 3",
      "B": "x = -2, 2",
      "C": "x = 1, 3",
      "D": "x = 0, 2"
    },
    "correct_answer": "A"
  },
  {
    "id": 50,
    "difficulty": "hard",
    "question": "Factorize: (x²+3x+2)(x²+7x+12) = 24 🏔️",
    "options": {
      "A": "(x²+5x+6)(x²+5x+4)=0",
      "B": "(x²+5x+8)(x²+5x)=0",
      "C": "(x²+5x+10)(x²+5x-2)=0",
      "D": "(x²+5x+12)(x²+5x-4)=0"
    },
    "correct_answer": "B"
  },
  {
    "id": 51,
    "difficulty": "hard",
    "question": "Solve: √(x+2√(x-1)) + √(x-2√(x-1)) = 2, x≥1 🌉",
    "options": {
      "A": "x = 1, 2",
      "B": "x = 1 only",
      "C": "x = 2 only",
      "D": "x = 5/4"
    },
    "correct_answer": "A"
  },
  {
    "id": 52,
    "difficulty": "hard",
    "question": "Factorize: 2(x²+1/x²) - 9(x+1/x) + 14 = 0, x≠0 🛸",
    "options": {
      "A": "[2(x+1/x)-7][(x+1/x)-2]=0",
      "B": "[(x+1/x)-7][2(x+1/x)-2]=0",
      "C": "[(x+1/x)-3][2(x+1/x)-7]=0",
      "D": "[(x+1/x)-1][2(x+1/x)-14]=0"
    },
    "correct_answer": "A"
  },
  {
    "id": 53,
    "difficulty": "hard",
    "question": "Solve: (x²+1/x²) - 3(x-1/x) - 2 = 0, x≠0 🎇",
    "options": {
      "A": "x = 1, -1, (3±√13)/2",
      "B": "x = 1, -1 only",
      "C": "x = (3±√13)/2 only",
      "D": "x = 0, 1"
    },
    "correct_answer": "A"
  },
  {
    "id": 54,
    "difficulty": "hard",
    "question": "Factorize: (x²+5x)² - 2(x²+5x) - 24 = 0 🌌",
    "options": {
      "A": "(x²+5x-6)(x²+5x+4)=0",
      "B": "(x²+5x-4)(x²+5x+6)=0",
      "C": "(x²+5x-8)(x²+5x+3)=0",
      "D": "(x²+5x-12)(x²+5x+2)=0"
    },
    "correct_answer": "A"
  },
  {
    "id": 55,
    "difficulty": "hard",
    "question": "Solve: √(x/(x-3)) + √((x-3)/x) = 5/2, x≠0,3 🎡",
    "options": {
      "A": "x = 4, 12/5",
      "B": "x = 4 only",
      "C": "x = 12/5 only",
      "D": "x = 3, 4"
    },
    "correct_answer": "A"
  },
  {
    "id": 56,
    "difficulty": "hard",
    "question": "Factorize: a²x² + (a²+b²)x + b² = 0 🔑",
    "options": {
      "A": "(ax+1)(ax+b²)=0",
      "B": "(ax+b)(ax+b)=0",
      "C": "(ax+b²)(x+1)=0",
      "D": "(a²x+b²)(x+1)=0"
    },
    "correct_answer": "D"
  },
  {
    "id": 57,
    "difficulty": "hard",
    "question": "Solve: |x-1| + |x-2| = x²-3x+2 🎭",
    "options": {
      "A": "x = 0, 1, 2, 3",
      "B": "x = 0, 3",
      "C": "x = 1, 2",
      "D": "x = (3±√5)/2"
    },
    "correct_answer": "A"
  },
  {
    "id": 58,
    "difficulty": "hard",
    "question": "Factorize: x⁴ + x² + 1 = 0 🤖",
    "options": {
      "A": "(x²+x+1)(x²-x+1)=0",
      "B": "(x²+1)² - x²=0",
      "C": "(x²+√3x+1)(x²-√3x+1)=0",
      "D": "A and B both"
    },
    "correct_answer": "D"
  },
  {
    "id": 59,
    "difficulty": "hard",
    "question": "Solve: √(1+√(1+√x)) = 2 🚁",
    "options": {
      "A": "x = 255",
      "B": "x = 256",
      "C": "x = 16",
      "D": "x = 225"
    },
    "correct_answer": "A"
  },
  {
    "id": 60,
    "difficulty": "hard",
    "question": "Factorize: (x²+3x+2)(x²+4x+3)(x²+5x+6) = 720 🔥",
    "options": {
      "A": "(x²+6x+8)(x²+6x+9)(x²+6x+10)=0",
      "B": "(x²+6x)(x²+6x+5)(x²+6x+10)=0",
      "C": "(x²+6x+5)(x²+6x+6)(x²+6x+7)=0",
      "D": "(x²+6x+9)(x²+6x+10)(x²+6x-8)=0"
    },
    "correct_answer": "B"
  }
  ]}