Capítulo 3. Respuestas

Operaciones entre expresiones algebraicas no racionales, ejercicios del 1 al 5.

  1. $\hspace{0.1cm}x^3-2x^2+8x+3\\[0.3cm]$
  2. $\hspace{0.1cm}x^3+4x+8$
  1. $\hspace{0.1cm}x^3-10x^2-4x+5$
  2. $\hspace{0.1cm}x^3-12x^2$
  1. $\hspace{0.1cm}x^2-1$

Productos notables ejercicios del 6 al 15.

  1. $\hspace{0.1cm}a^4 b^4+6a^2 b^2-7\\[0.3cm]$
  2. $\hspace{0.1cm}x^6 y^6+2x^3 y^3-48$
  3. $\hspace{0.1cm} a^{2x}+2a^x b^{x+1}+b^{2x+2}$
  4. $\hspace{0.1cm}x^{2a+2}-6x^{2a-1}+9x^{2a-4}$
  1. $\hspace{0.1cm}9x^{2a}-25y^{2m}$
  2. $\hspace{0.1cm}a^{2x+2}-4b^{2x-2}$
  3. $\hspace{0.1cm}a^6-6a^4 b+12a^2 b^2-8b^3$
  1. $\hspace{0.1cm}8x^3+36x^2 y+54xy^2+27y^3$
  2. $\hspace{0.1cm} \cfrac{9}{16} a^4- \cfrac{3}{4} a^3+\cfrac{29}{20} a^2-\cfrac{4}{5} a+\cfrac{16}{25}$
  3. $\hspace{0.1cm}9-36a+42 a^2-18a^3+13a^4-2a^5+ a^6$

Factoriza totalmente los siguientes polinomios por el método adecuado, ejercicios del 16 al 35.

  1. $\hspace{0.1cm}\left(x+1\right)\left(ax+a+1\right)$
  2. $\hspace{0.1cm}\left(a+b\right)\left(a^2-ab+b^2+a-b\right)$
  3. $\hspace{0.1cm}\left(y^2+4\right)\left(y+2\right)\left(y-2\right)$
  4. $\hspace{0.1cm}\left(2a^n+b^n\right)\left(2a^n-b^n\right)\cdot\\\left(4a^2n-2a^n b^n+b^2n\right)\cdot\\\left(4a^2n+2a^n b^n+b^2n\right)$
  5. $\hspace{0.1cm}\left(3^n-5\right)\left(3^n+4\right)$
  6. $\hspace{0.1cm}\left(a^2+1\right)\left(1-b\right)$
  7. $\hspace{0.1cm}\left(t^2+1\right)\left(t^4+1\right)$
  1. $\hspace{0.1cm}\left(x-y^n\right)\left(2x+y^n\right)$
  2. $\hspace{0.1cm}\left(x-4y+6a-b\right)\left(x-4y-6a+b\right)$
  3. $\hspace{0.1cm}\left(2x-1\right)\left(x+1\right)\left(4x^2+2x+1\right)\cdot\\\left(x^2-x+1\right)$
  4. $\hspace{0.1cm}\left(5+x-4y\right)\left(5-x+4y\right)$
  5. $\hspace{0.1cm}\left(7x^2+5x-3y\right)\left(7x^2-5x+3y\right)$
  6. $\hspace{0.1cm}\left(2a+2b+x\right)\left(2b-x\right)$
  7. $\hspace{0.1cm}\left(4x^2+8x+9\right)\left(4x^2-8x+9\right)$
  1. $\hspace{0.1cm}\left(x^2+9x-6\right)\left(x^2-9x-6\right)$
  2. $\hspace{0.1cm}\left(2a^4-7b^4+5a^2 b^2\right)\left(2a^4-7b^4-5a^2 b^2\right)$
  3. $\hspace{0.1cm}\left(x^4+1\right)\left(x^2+1\right)\left(x+1\right)\left(x-1\right)$
  4. $\hspace{0.1cm}\left(2x-y\right)\left(2x+y\right)\left(4x^2+2xy+y^2\right)\cdot\\\left(4x^2-2xy+y^2\right)$
  5. $\hspace{0.1cm}\left(4 +a^2\right)\left(16 -4a^2 +a^4\right)$
  6. $\hspace{0.1cm}\left(2a +3b^2\right)\left(4a^2 -6ab^2 +9b^4\right) $

Solución ejercicios del 36 al 40. División de polinomios.

  1. $\hspace{0.1cm}\text{Cocciente:}\;3a^{x+3}-a^{x+2}+a^{x+1}\\\text{\;Residuo:}\;0$
  2. $\hspace{0.1cm}\text{Cociente:}\;4x^2+2x\\\text{\;Residuo:}\ -7x+1$
  3. $\hspace{0.1cm}\text{Cociente:}\;2x+2\\\text{\;Residuo:}\; -3x$
  1. $\hspace{0.1cm}\text{Cociente:}\;-x-1\\\text{\;Residuo:}\; -x+11$
  2. $\hspace{0.1cm}\text{Cociente:}\;-2x+12\\\text{\;Residuo:}\;74x-54$

Solución ejercicios del 41 al 45. racionalización de denominadores.

  1. $\hspace{0.1cm}\sqrt{x}+\sqrt{y}$
  2. $\hspace{0.1cm}\cfrac{\sqrt[3]{x^2}+\sqrt[3]{xy}+\sqrt[3]{y^2}}{x-y}$
  3. $\hspace{0.1cm}\sqrt{a^4-1}+1$
  1. $\hspace{0.1cm}\cfrac{2\left(a\sqrt{x}-3\sqrt{a}\right)}{ax-9}$
  2. $\hspace{0.1cm}\sqrt{x^2-1}+1$