S1

{
   "voice_prompt": "",
   "manuscript": {
       "title": {
           "text": "How Do You Factorize Quadratic Expressions?",
           "audio": "How do you factorize quadratic expressions?"
       },
       "description": {
           "text": "Find the roots using the quadratic formula, factoring, or another method. Then write the expression as: a(x - x_1)(x - x_2).
              ",
           "audio": "Find the roots using the quadratic formula, factoring, or another method. Then write the expression as: a times x minus the first root, times x minus the second root."
       },
       "scenes": [
           {
               "text": "To do this, you use the roots of the quadratic expression. Once you have them, you can rewrite the expression as a product of two brackets. The general rule is: the quadratic becomes a times x minus the first root, times x minus the second root. This is useful to know when analyzing algebraic expressions and graphing quadratic functions.",
               "latex": "ax^2 + bx + c = a(x - x_1)(x - x_2)"
           },
           {
               "text": "Let's factor two x squared minus four x minus six. Your goal is to rewrite it as a product of two brackets. To do that, first find the roots. These are the values of x that make the expression equal zero. You can use the quadratic formula, factoring, or another method.",
               "latex": "2x^2 - 4x - 6"
           },
           {
               "text": "Let's use the quadratic formula. a equals 2, b equals minus 4 and c equals minus 6. Substituting these values into the formula gives.",
               "latex": "abc-formula....."
           },
           {      
               
               "text": " So, the solutions are x_1 equals 3 and x_2 equals minus 1.",
               "latex": "x_1 = 3, \\quad x_2 = -1"
           },
           {
               "text": "Now that you have the roots, plug them into the factoring formula. That gives you a times x minus the first root, times x minus the second root.",
               "latex": "a(x - 3)(x + 1)"
           },
           {
               "text": "In this example, a is two, so you get: two times x minus three, times x plus one.",
               "latex": "2x^2 - 4x - 6 = 2(x - 3)(x + 1)"
           }
       ],
       "outro": {
           "text": "Find the roots using the quadratic formula, factoring, or another method. Then write the expression as: a(x - x_1)(x - x_2).
              ",
           "audio": "Find the roots using the quadratic formula, factoring, or another method. Then write the expression as: a times x minus the first root, times x minus the second root."
       }
   }
}

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