{
  "unit": 2,
  "title": "Polynomial Functions & Complex Numbers",
  "terms": [
    {
      "en": "polynomial",
      "es": "polinomio",
      "fr": "polynôme",
      "ar": "كثيرة حدود",
      "pt": "polinômio",
      "definition": "A finite sum of nonnegative integer powers of a variable with coefficients."
    },
    {
      "en": "coefficient",
      "es": "coeficiente",
      "fr": "coefficient",
      "ar": "معامل",
      "pt": "coeficiente",
      "definition": "A numerical factor multiplying a variable term."
    },
    {
      "en": "degree",
      "es": "grado",
      "fr": "degré",
      "ar": "درجة كثيرة الحدود",
      "pt": "grau",
      "definition": "The highest exponent of the variable in a nonzero polynomial."
    },
    {
      "en": "polynomial term",
      "es": "término polinómico",
      "fr": "terme polynomial",
      "ar": "حد كثير الحدود",
      "pt": "termo polinomial",
      "definition": "A coefficient multiplied by variables raised to nonnegative integer powers."
    },
    {
      "en": "equivalent polynomial forms",
      "es": "formas polinómicas equivalentes",
      "fr": "formes polynomiales équivalentes",
      "ar": "صيغ كثيرة حدود متكافئة",
      "pt": "formas polinomiais equivalentes",
      "definition": "Expressions producing identical values for all inputs in their common domain."
    },
    {
      "en": "power function",
      "es": "función potencia",
      "fr": "fonction puissance",
      "ar": "دالة القوة",
      "pt": "função potência",
      "definition": "A function of the form f(x)=a x^n for constant a and exponent n."
    },
    {
      "en": "leading coefficient",
      "es": "coeficiente principal",
      "fr": "coefficient dominant",
      "ar": "المعامل الرئيسي",
      "pt": "coeficiente líder",
      "definition": "The coefficient of the highest-degree nonzero term."
    },
    {
      "en": "end behavior",
      "es": "comportamiento en los extremos",
      "fr": "comportement aux extrémités",
      "ar": "سلوك الدالة عند الأطراف",
      "pt": "comportamento nas extremidades",
      "definition": "How a graph behaves as x approaches positive or negative infinity."
    },
    {
      "en": "imaginary unit",
      "es": "unidad imaginaria",
      "fr": "unité imaginaire",
      "ar": "الوحدة التخيلية",
      "pt": "unidade imaginária",
      "definition": "The number i satisfying i²=-1."
    },
    {
      "en": "powers of i",
      "es": "potencias de i",
      "fr": "puissances de i",
      "ar": "قوى العدد التخيلي i",
      "pt": "potências de i",
      "definition": "The repeating cycle i, -1, -i, 1 for successive positive integer powers."
    },
    {
      "en": "complex number",
      "es": "número complejo",
      "fr": "nombre complexe",
      "ar": "عدد مركب",
      "pt": "número complexo",
      "definition": "A number of the form a+bi, where a and b are real."
    },
    {
      "en": "complex conjugate",
      "es": "conjugado complejo",
      "fr": "conjugué complexe",
      "ar": "المرافق المركب",
      "pt": "conjugado complexo",
      "definition": "The number a-bi corresponding to a+bi."
    },
    {
      "en": "complex addition",
      "es": "suma de números complejos",
      "fr": "addition des nombres complexes",
      "ar": "جمع الأعداد المركبة",
      "pt": "adição de números complexos",
      "definition": "Adding real parts and imaginary parts separately."
    },
    {
      "en": "complex multiplication",
      "es": "multiplicación de números complejos",
      "fr": "multiplication des nombres complexes",
      "ar": "ضرب الأعداد المركبة",
      "pt": "multiplicação de números complexos",
      "definition": "Distributing factors and using i²=-1."
    },
    {
      "en": "quadratic discriminant",
      "es": "discriminante cuadrático",
      "fr": "discriminant quadratique",
      "ar": "مميز المعادلة التربيعية",
      "pt": "discriminante quadrático",
      "definition": "The value b²-4ac that determines the type of roots of ax²+bx+c=0."
    },
    {
      "en": "complex roots",
      "es": "raíces complejas",
      "fr": "racines complexes",
      "ar": "جذور مركبة",
      "pt": "raízes complexas",
      "definition": "Solutions of a polynomial equation that may have nonzero imaginary parts."
    },
    {
      "en": "complex plane",
      "es": "plano complejo",
      "fr": "plan complexe",
      "ar": "المستوى المركب",
      "pt": "plano complexo",
      "definition": "A coordinate plane representing a+bi at the point (a,b)."
    },
    {
      "en": "modulus",
      "es": "módulo",
      "fr": "module",
      "ar": "المقياس المطلق للعدد المركب",
      "pt": "módulo",
      "definition": "The distance of a+bi from the origin, equal to sqrt(a²+b²)."
    },
    {
      "en": "fundamental theorem of algebra",
      "es": "teorema fundamental del álgebra",
      "fr": "théorème fondamental de l'algèbre",
      "ar": "النظرية الأساسية في الجبر",
      "pt": "teorema fundamental da álgebra",
      "definition": "Every nonconstant one-variable polynomial with complex coefficients has a complex root."
    },
    {
      "en": "complete factorization",
      "es": "factorización completa",
      "fr": "factorisation complète",
      "ar": "التحليل الكامل إلى عوامل",
      "pt": "fatoração completa",
      "definition": "Writing a degree-n complex polynomial as a product of n linear factors counting multiplicity."
    }
  ],
  "schema_version": "1.1"
}