{
  "unit": 3,
  "title": "Polynomial Equations, Division & Graphs",
  "terms": [
    {
      "en": "polynomial long division",
      "es": "división larga de polinomios",
      "fr": "division euclidienne des polynômes",
      "ar": "القسمة المطولة لكثيرات الحدود",
      "pt": "divisão longa de polinômios",
      "definition": "Finding quotient and remainder by repeated polynomial division."
    },
    {
      "en": "dividend",
      "es": "dividendo",
      "fr": "dividende",
      "ar": "المقسوم",
      "pt": "dividendo",
      "definition": "The polynomial being divided."
    },
    {
      "en": "divisor",
      "es": "divisor",
      "fr": "diviseur",
      "ar": "المقسوم عليه",
      "pt": "divisor",
      "definition": "A nonzero polynomial used to divide another."
    },
    {
      "en": "synthetic division",
      "es": "división sintética",
      "fr": "division synthétique",
      "ar": "القسمة التركيبية",
      "pt": "divisão sintética",
      "definition": "Coefficient shortcut for division by x-c."
    },
    {
      "en": "Horner method",
      "es": "método de Horner",
      "fr": "méthode de Horner",
      "ar": "طريقة هورنر",
      "pt": "método de Horner",
      "definition": "Evaluating a polynomial by nested multiplications."
    },
    {
      "en": "remainder",
      "es": "resto",
      "fr": "reste",
      "ar": "الباقي",
      "pt": "resto",
      "definition": "The leftover polynomial with degree below that of the divisor."
    },
    {
      "en": "remainder theorem",
      "es": "teorema del resto",
      "fr": "théorème du reste",
      "ar": "نظرية الباقي",
      "pt": "teorema do resto",
      "definition": "The remainder of f(x) divided by x-c equals f(c)."
    },
    {
      "en": "factor theorem",
      "es": "teorema del factor",
      "fr": "théorème du facteur",
      "ar": "نظرية العامل",
      "pt": "teorema do fator",
      "definition": "x-c is a factor of f(x) precisely when f(c)=0."
    },
    {
      "en": "rational root theorem",
      "es": "teorema de la raíz racional",
      "fr": "théorème des racines rationnelles",
      "ar": "نظرية الجذر النسبي",
      "pt": "teorema da raiz racional",
      "definition": "For integer coefficients a reduced root p/q requires p to divide the constant and q the leading coefficient."
    },
    {
      "en": "candidate rational root",
      "es": "posible raíz racional",
      "fr": "racine rationnelle candidate",
      "ar": "جذر نسبي محتمل",
      "pt": "possível raiz racional",
      "definition": "A rational number to test from the rational-root theorem."
    },
    {
      "en": "polynomial equation",
      "es": "ecuación polinómica",
      "fr": "équation polynomiale",
      "ar": "معادلة كثيرة حدود",
      "pt": "equação polinomial",
      "definition": "An equation expressible as f(x)=0 for a polynomial f."
    },
    {
      "en": "factoring",
      "es": "factorización",
      "fr": "factorisation",
      "ar": "التحليل إلى عوامل",
      "pt": "fatoração",
      "definition": "Rewriting an expression as a product."
    },
    {
      "en": "higher-degree polynomial",
      "es": "polinomio de grado superior",
      "fr": "polynôme de degré supérieur",
      "ar": "كثيرة حدود من درجة أعلى",
      "pt": "polinômio de grau superior",
      "definition": "A polynomial of degree at least three."
    },
    {
      "en": "polynomial zero",
      "es": "cero polinómico",
      "fr": "zéro polynomial",
      "ar": "صفر كثيرة الحدود",
      "pt": "zero polinomial",
      "definition": "An input r such that f(r)=0."
    },
    {
      "en": "multiplicity",
      "es": "multiplicidad",
      "fr": "multiplicité",
      "ar": "تعدد الجذر",
      "pt": "multiplicidade",
      "definition": "How many times a root appears as a linear factor."
    },
    {
      "en": "graph crossing",
      "es": "cruce del eje x",
      "fr": "croisement de l'axe x",
      "ar": "عبور محور السينات",
      "pt": "cruzamento do eixo x",
      "definition": "A real root with odd multiplicity crosses the x-axis."
    },
    {
      "en": "polynomial regression",
      "es": "regresión polinómica",
      "fr": "régression polynomiale",
      "ar": "الانحدار بكثيرة حدود",
      "pt": "regressão polinomial",
      "definition": "Fitting polynomial coefficients to observed data."
    },
    {
      "en": "interpolation",
      "es": "interpolación",
      "fr": "interpolation",
      "ar": "الاستيفاء",
      "pt": "interpolação",
      "definition": "Estimating within the measured data range."
    },
    {
      "en": "extrapolation",
      "es": "extrapolación",
      "fr": "extrapolation",
      "ar": "الاستقراء خارج البيانات",
      "pt": "extrapolação",
      "definition": "Predicting beyond the observed data range."
    }
  ],
  "schema_version": "1.1"
}