10th Grade
How Do You Factorize Quadratic Expressions?
{
"voice_prompt": "",
"manuscript": {
"title": {
"text": "How Do You Factorize a Quadratic Expression When the Roots Are Known?",
"audio": "How do you factorize a quadratic expression when the roots are known?"
},
"description": {
"text": "If you already know the roots of a quadratic expression, you can write it as:",
"audio": "If you already know the roots of a quadratic expression, you can write it as A, times x minus the first root, times x minus the second root."
},
"scenes": [
{
"text": " ",
"latex": "a(x-x_1)(x-x_2)"
},
{
"text": "Let’s look at an example. We’ll factor the quadratic expression 2x squared minus 4x minus 6.",
"latex": "2x^2 - 4x - 6"
},
{
"text": "To factor it, you write the expression as, A, times x minus the first root, times x minus the second root.",
"latex": "2x^2 - 4x - 6 = a(x-x_1)(x-x_2)"
},
{
"text": "This time, you already know the roots. They are 3 and minus 1.",
"latex": "2x^2 - 4x - 6 = a(x-x_1)(x-x_2) \\quad x_1 = 3, \\quad x_2 = -1"
},
{
"text": "Now that you have the roots, plug them into the factoring formula. x one becomes 3 and x two becomes -1",
"latex": "2x^2 - 4x - 6 = a(x - 3)(x - ( -1))"
},
{
"text": "minus miuns 1 equals plus 1",
"latex": "2x^2 - 4x - 6 = 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": "If you already know the roots of a quadratic expression, you can factor it by plugging them into brackets.",
"audio": "If you already know the roots of a quadratic expression, you can factor it by plugging them into brackets."
}
}
}
