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Paula Soler
21/5/2023
Matemáticas
Polinomios
Polynomials and algebraic fractions are fundamental concepts in algebra. This guide covers key topics like calculating numerical values, performing operations, factoring polynomials, and working with algebraic fractions. Students will learn essential skills for manipulating polynomial expressions and solving related problems.
21/5/2023
792
This section delves into finding roots of polynomials and the process of factorization.
A number "a" is a root of a polynomial P(x) if P(a) = 0.
Example: The text demonstrates how to check if certain values are roots of the polynomial P(x) = 3x² - 5x + 2.
Factorization involves expressing a polynomial as a product of polynomials of lower degree. If a polynomial cannot be factored, it is called irreducible.
Highlight: The guide provides multiple methods for factoring polynomials, including finding common factors, using notable identities, solving quadratic equations, and applying Ruffini's rule. This comprehensive approach is valuable for students learning factorizar polinomios.
Example: The text walks through the factorization of P(x) = 2x⁴ + x³ - 8x² - x + 6 using Ruffini's rule.
This chapter introduces the concept of algebraic fractions and operations involving them.
An algebraic fraction is a fraction with a polynomial in the denominator. The text explains how to simplify algebraic fractions through factorization.
Example: The guide provides examples of simplifying algebraic fractions like (x² + 2x + 1) / (x² - 1).
The chapter covers addition, subtraction, multiplication, and division of algebraic fractions.
Highlight: Step-by-step examples are provided for each operation, helping students understand how to perform operaciones con polinomios suma, resta, multiplicación y división.
The final section of the chapter focuses on polynomial division and the application of Ruffini's rule.
When dividing polynomials P(x) ÷ Q(x), the result is expressed as P(x) = Q(x) · C(x) + R(x), where C(x) is the quotient and R(x) is the remainder.
Example: The text demonstrates long division of polynomials, such as (2x⁴ - 7x³ + 8x² - 6x + 3) ÷ (x² - 3x + 2).
Ruffini's rule is introduced as a method for dividing polynomials by linear factors of the form (x ± a).
Highlight: The guide explains how to apply Ruffini's rule, which is particularly useful for factorización de polinomios Ruffini.
Example: The text provides an example of using Ruffini's rule to divide (2x³ - 41x² - 10x + 3) by (x - 2).
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Paula Soler
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Polynomials and algebraic fractions are fundamental concepts in algebra. This guide covers key topics like calculating numerical values, performing operations, factoring polynomials, and working with algebraic fractions. Students will learn essential skills for manipulating polynomial expressions and solving related problems.
Acceso a todos los documentos
Mejora tus notas
Únete a millones de estudiantes
Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.
This section delves into finding roots of polynomials and the process of factorization.
A number "a" is a root of a polynomial P(x) if P(a) = 0.
Example: The text demonstrates how to check if certain values are roots of the polynomial P(x) = 3x² - 5x + 2.
Factorization involves expressing a polynomial as a product of polynomials of lower degree. If a polynomial cannot be factored, it is called irreducible.
Highlight: The guide provides multiple methods for factoring polynomials, including finding common factors, using notable identities, solving quadratic equations, and applying Ruffini's rule. This comprehensive approach is valuable for students learning factorizar polinomios.
Example: The text walks through the factorization of P(x) = 2x⁴ + x³ - 8x² - x + 6 using Ruffini's rule.
Acceso a todos los documentos
Mejora tus notas
Únete a millones de estudiantes
Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.
This chapter introduces the concept of algebraic fractions and operations involving them.
An algebraic fraction is a fraction with a polynomial in the denominator. The text explains how to simplify algebraic fractions through factorization.
Example: The guide provides examples of simplifying algebraic fractions like (x² + 2x + 1) / (x² - 1).
The chapter covers addition, subtraction, multiplication, and division of algebraic fractions.
Highlight: Step-by-step examples are provided for each operation, helping students understand how to perform operaciones con polinomios suma, resta, multiplicación y división.
Acceso a todos los documentos
Mejora tus notas
Únete a millones de estudiantes
Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.
The final section of the chapter focuses on polynomial division and the application of Ruffini's rule.
When dividing polynomials P(x) ÷ Q(x), the result is expressed as P(x) = Q(x) · C(x) + R(x), where C(x) is the quotient and R(x) is the remainder.
Example: The text demonstrates long division of polynomials, such as (2x⁴ - 7x³ + 8x² - 6x + 3) ÷ (x² - 3x + 2).
Ruffini's rule is introduced as a method for dividing polynomials by linear factors of the form (x ± a).
Highlight: The guide explains how to apply Ruffini's rule, which is particularly useful for factorización de polinomios Ruffini.
Example: The text provides an example of using Ruffini's rule to divide (2x³ - 41x² - 10x + 3) by (x - 2).
Acceso a todos los documentos
Mejora tus notas
Únete a millones de estudiantes
Al registrarte aceptas las Condiciones del servicio y la Política de privacidad.
This chapter covers fundamental concepts related to polynomials and algebraic fractions, providing a comprehensive overview for students.
The numerical value of a polynomial P(x) at x=a is denoted as P(a), which is the result of substituting x with a in the polynomial expression.
Example: Calculate the numerical value of P(x) = x³ - 3x² + x - 1 for x = 1, x = -2, and x = 1/3.
This section covers addition, subtraction, and multiplication of polynomials, as well as extracting common factors.
Highlight: The text provides step-by-step examples for performing operations with polynomials, which is crucial for understanding suma, resta, multiplicación y división de polinomios.
The chapter introduces the concept of polynomial powers and notable identities, including the square and cube of binomials.
Definition: The power of a polynomial [P(x)]ⁿ is the product of P(x) with itself n times.
Vocabulary: Pascal's Triangle is introduced as a tool for finding coefficients in polynomial expansions.
valoración media de la app
A los alumnos les encanta Knowunity
en las listas de aplicaciones educativas de 17 países
alumnos han subido contenidos escolares
Usuario de iOS
Javi, usuario de iOS
Mari, usuario de iOS
