unidad 1- Profundizar y contextualizar el conocimiento de la Unidad 1.
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This document provides an overview of algebra, trigonometry, and analytical geometry concepts including: algebraic expressions, polynomials, factorization methods, and rational algebraic expressions. Examples are given for multiplying polynomials, synthetic division of polynomials, factorization cases like common factors, difference of squares, and sum or difference of cubes. Factorization techniques are described as decomposing an expression into factors in the form of a product to simplify fractions.
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March 18, 2015
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unidad 1- Profundizar y contextualizar el conocimiento de la Unidad 1.
- 1. ALGEBRA, TRIGONOMETRÍAY GEOMETRÍA ANALÍTICA Paso 2 profundizar y contextualizar el conocimiento de la unidad 1 • Nombre : Yoli Yulieth Latorre Gomez • Código: 1085689178 • Tutor: Henry Albeiro Sáenz • Grupo: 551108_20
- 2. ELEMENTOS ,CARACTERÍSTICAS Y PROCEDIMIENTOS DE LA UNIDAD 1 -EXPRESIONES ALGEBRAICAS -POLINOMIOS -CASOS DE FACTORIZACIÓN -EXPRESIONES ALGEBRAICAS RACIONALES
- 4. EJEMPLOS: • . (𝑥 + 2)(2𝑥 − 3) + 2(3 − 𝑥2 ) Multiplicamos los paréntesis. • =2𝑥2 − 3𝑥 + 4𝑥 − 6 + 2(3 − 𝑥2 ) • =2𝑥2 − 3𝑥 + 4𝑥 − 6 + 6 − 2𝑥2 • =2𝑥2 − 2𝑥2 − 3𝑥 + 4𝑥 − 6 + 6 Ordenamos según su parte literal para poder realizar la operación correspondiente. • =0 − 3𝑥 + 4𝑥 − 6 + 6 • =𝑥 − 6 + 6 • =𝑥 − 0 • =x Encontramos la solución a esta expresión algebraica.
- 5. POLINOMIOS • Estos son expresiones algebraicas, en los cuales intervienen números y letras, relacionas mediante sumas o restas de monomios; sus variables son letras ya que asumen cualquier valor y sus números son llamados coeficientes.
- 6. DIVISIÓN SINTÉTICA DE POLINOMIOS La división sintética es un método abreviado para dividir polinomios, donde se divide el coeficiente de los polinomios, eliminando las variables y los exponentes
- 7. . 6𝑥4 + 7𝑥3 − 6𝑥2 + 7𝑥 − 2 ÷ (3𝑥 − 1) =−6𝑥4 + 2𝑥3 2𝑥3 + 3𝑥2 − 𝑥 + 2 __________________________ = / 9𝑥3 − 6𝑥2 + 7𝑥 − 2 = −9𝑥3 + 3𝑥2 ____________________________ = / −3𝑥2 + 7𝑥 − 2 = 3𝑥2 − 𝑥 _____________________________ = / 6𝑥 − 2 = −6𝑥 + 2 ________________________________ = / / EJEMPLO:
- 8. CASOS DE FACTORIZACIÓN • Es una técnica que consiste en la descomposición en factores de una expresión algebraica (que puede ser un número, una suma o resta, una matriz, un polinomio, etc.) en forma de producto. Algunas clases de factorización son: Factor común. Factor común por agrupación de términos. Diferencia de cuadrados. Suma o diferencia de cubos. Trinomio cuadrado perfecto. Trinomio de la forma 𝑥2 + 𝑏𝑥 + 𝑐 Trinomio de la forma 𝑎𝑥2 + 𝑏𝑥 + 𝑐 Hay diferentes métodos de factorizar dependiendo de los objetos matemáticos estudiados, el Objetivo es simplificar una fracción en grupos de mas fácil comprensión que reciben el nombre de factor
- 9. EJEMPLOS • 18𝑎3 − 8𝑎 ; 3𝑚3 − 6𝑚2 + 15𝑚 • =2𝑎 × (9𝑎2 − 4) ; 3𝑚 × (𝑚2 − 2𝑚 + 5) • =2𝑎 × (3𝑎 − 2) × (3𝑎 + 2)
- 10. EXPRESIONES ALGEBRAICAS RACIONALES: • Son aquellas en las cuales algunas de sus variables forman parte del denominador o figuran en el numerador con exponente entero. • Por ejemplo: 𝑥 + 2 𝑦 ; 2𝑎−4 + 5
- 11. BIBLIOGRAFIAS • Carlos, L. (2020). OVI Unidad 1: lenguaje algebraico. Bogotá D.C. Universidad Nacional Abierta y a Distancia. Obtenido y recuperado de https://repository.unad.edu.co/handle/10596/36117 • Elles, L. (2018). OVI Clasificación de las Expresiones algebraicas [Archivo de video]. Recuperado de https://www.youtube.com/watch?v=V-_5W9MxeO4&feature=youtu.be Video que trata sobre el concepto de expresiones algebraicas. • Algebra Simbólica. Moreno Y. (2014). [OVI]. Algebra Simbólica. Bogotá D.C. Universidad Nacional Abierta y a Distancia. [Archivo de video]. Recuperado de: http://hdl.handle.net/10596/11601