Ejercicios sección 3.3

En los ejercicios 1 al 10, use la división larga entre los polinomios indicados para determinar el cociente y el residuo.

  1. $\hspace{0.1cm}f_{\left(x\right)}=5x^2+2x-3;\;\; g_{\left(x\right)}=x^2+1\\[0.2cm]$
  2. $\hspace{0.1cm}f_{\left(x\right)}=14x^3-12x^2+6;\;\; g_{\left(x\right)}=x^2-1\\[0.2cm]$
  3. $\hspace{0.1cm}f_{\left(x\right)}=x^3+x^2+x+1;\;\; g_{\left(x\right)}=\left(2x+1\right)^2\\[0.2cm]$
  4. $\hspace{0.1cm}f_{\left(x\right)}=x^4+8;\;\; g_{\left(x\right)}=x^3+2x-1\\[0.2cm]$
  5. $\hspace{0.1cm}f_{\left(x\right)}=5x^6-x^5+10x^4+3x^2-2x+4;\\\; g_{\left(x\right)}=x^2+x-1\\[0.2cm]$
  1. $\hspace{0.1cm}f_{\left(x\right)}=2x^4-x^3-3x^2+7x-12;\;\; g_{\left(x\right)}=x^2-3\\[0.2cm]$
  2. $\hspace{0.1cm}f_{\left(x\right)}=3x^4+2x^3-x^2-x-6;\;\; g_{\left(x\right)}=x^2+1\\[0.2cm]$
  3. $\hspace{0.1cm}f_{\left(x\right)}=3x^3-5x^2-4x-8;\;\; g_{\left(x\right)}=2x^2+x\\[0.2cm]$
  4. $\hspace{0.1cm}f_{\left(x\right)}=x^3-3x+9;\;\; g_{\left(x\right)}=-5x^2+3\\[0.2cm]$
  5. $\hspace{0.1cm}f_{\left(x\right)}=7x^2+3x+10;\;\; g_{\left(x\right)}=x^2-x+10\\[0.2cm]$

En los ejercicios 11 al 20, use la división sintética (Ruffini) entre los polinomios indicados para determinar el cociente y el residuo.

  1. $\hspace{0.1cm}f_{\left(x\right)}=2x^3-3x^2+4x-5;\;\; g_{\left(x\right)}=x-2\\[0.2cm]$
  2. $\hspace{0.1cm}f_{\left(x\right)}=3x^3-4x^2-x+8;\;\; g_{\left(x\right)}=x+4\\[0.2cm]$
  3. $\hspace{0.1cm}f_{\left(x\right)}=5x^3-6x^2+15;\;\; g_{\left(x\right)}=x-4\\[0.2cm]$
  4. $\hspace{0.1cm}f_{\left(x\right)}=-2x^4+10x-3;\;\; g_{\left(x\right)}=x-3\\[0.2cm]$
  5. $\hspace{0.1cm}f_{\left(x\right)}=9x^3-6x^2+3x-4;\\\; g_{\left(x\right)}=x-\frac{1}{3}\\[0.2cm]$
  1. $\hspace{0.1cm}f_{\left(x\right)}=4x^2-8x+6;\;\; g_{\left(x\right)}=x-\frac{1}{2}\\[0.2cm]$
  2. $\hspace{0.1cm}f_{\left(x\right)}=4x^3-3x^2+2x+4;\;\; g_{\left(x\right)}=x-7\\[0.2cm]$
  3. $\hspace{0.1cm}f_{\left(x\right)}=4x^4+3x^3-x^2-5x-6;\;\; g_{\left(x\right)}=x+3\\[0.2cm]$
  4. $\hspace{0.1cm}f_{\left(x\right)}=2x^6+3x^3-4x^2-1;\;\; g_{\left(x\right)}=x+1\\[0.2cm]$
  5. $\hspace{0.1cm}f_{\left(x\right)}=x^3-\left(2+\sqrt{3}\right)x^2+3\sqrt{3x}-3;\;\; g_{\left(x\right)}=x-\sqrt{3}\\[0.2cm]$