Respuestas sección 3.3

Ejercicios 1 al 10. División larga entre los polinomios.

  1. $\hspace{0.1cm}\text{Cociente=\;}5\\\text{\;Residuo=\;}2x-5\\[0.2cm]$
  2. $\hspace{0.1cm}\text{Cociente=\;}14x-12\\\text{\;Residuo=\;}14x-6\\[0.2cm]$
  3. $\hspace{0.1cm}\text{Cociente=\;}\frac{1}{4}x\\[0.2cm]\text{\;Residuo=\;}\frac{3}{4}x+1\\[0.2cm]$
  4. $\hspace{0.1cm}\text{Cociente=\;}x\\\text{\;Residuo=\;}-2x^2+x+8\\[0.2cm]$
  5. $\hspace{0.1cm}\text{Cociente=\;}5x^4-6x^3+21x^2-27x+51\\\text{\;Residuo=\;}-80x+55\\[0.2cm]$
  1. $\hspace{0.1cm}\text{Cociente=\;}2x^2-x+3\\\text{\;Residuo=\;}4x-3\\[0.2cm]$
  2. $\hspace{0.1cm}\text{Cociente=\;}3x^2+2x-4\\\text{\;Residuo=\;}-3x-2\\[0.2cm]$
  3. $\hspace{0.1cm}\text{Cociente=\;}\frac{3}{2}x-\frac{13}{4}\\[0.2cm]\text{\;Residuo=\;}-\frac{3}{4}x-8\\[0.2cm]$
  4. $\hspace{0.1cm}\text{Cociente=\;}-\frac{1}{5}x\\[0.2cm]\text{\;Residuo=\;}-\frac{12}{5}x+9\\[0.2cm]$
  5. $\hspace{0.1cm}\text{Cociente=\;}7\\\text{\;Residuo=\;}10x-60\\[0.2cm]$

Ejercicios 1 al 10. División sintética (Ruffini) entre los polinomios.

  1. $\hspace{0.1cm}\text{Cociente=\;}2x^2+x+6\\\text{\;Residuo=\;}7\\[0.2cm]$
  2. $\hspace{0.1cm}\text{Cociente=\;}3x^2-16x+63\\\text{\;Residuo=\;}-244\\[0.2cm]$
  3. $\hspace{0.1cm}\text{Cociente=\;}5x^2+14x+56\\[0.2cm]\text{\;Residuo=\;}239\\[0.2cm]$
  4. $\hspace{0.1cm}\text{Cociente=\;}-2x^3-6x^2-18x-44\\\text{\;Residuo=\;}-135\\[0.2cm]$
  5. $\hspace{0.1cm}\text{Cociente=\;}9x^2-3x+2\\\text{\;Residuo=\;}-\frac{10}{3}\\[0.2cm]$
  1. $\hspace{0.1cm}\text{Cociente=\;}4x-6\\\text{\;Residuo=\;}3\\[0.2cm]$
  2. $\hspace{0.1cm}\text{Cociente=\;}4x^2+25x+177\\\text{\;Residuo=\;}1243\\[0.2cm]$
  3. $\hspace{0.1cm}\text{Cociente=\;}4x^3-9x^2+26x-83\\[0.2cm]\text{\;Residuo=\;}243\\[0.2cm]$
  4. $\hspace{0.1cm}\text{Cociente=\;}2x^5-2x^4+2x^3+x^2-5x+5\\[0.2cm]\text{\;Residuo=\;}-6\\[0.2cm]$
  5. $\hspace{0.1cm}\text{Cociente=\;}x^2+\left(2+2\sqrt{3}\right)x+\left(2\sqrt{3}+6\right)\\\text{\;Residuo=\;}3\sqrt{x}+\left(3+6\sqrt{3}\right)\\[0.2cm]$