Capítulo 3. Respuestas

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

  1. x3−2x2+8x+3\hspace{0.1cm}x^3-2x^2+8x+3\\[0.3cm]
  2. x3+4x+8\hspace{0.1cm}x^3+4x+8
  1. x3−10x2−4x+5\hspace{0.1cm}x^3-10x^2-4x+5
  2. x3−12x2\hspace{0.1cm}x^3-12x^2
  1. x2−1\hspace{0.1cm}x^2-1

Productos notables ejercicios del 6 al 15.

  1. a4b4+6a2b2−7\hspace{0.1cm}a^4 b^4+6a^2 b^2-7\\[0.3cm]
  2. x6y6+2x3y3−48\hspace{0.1cm}x^6 y^6+2x^3 y^3-48
  3. a2x+2axbx+1+b2x+2\hspace{0.1cm} a^{2x}+2a^x b^{x+1}+b^{2x+2}
  4. x2a+2−6x2a−1+9x2a−4\hspace{0.1cm}x^{2a+2}-6x^{2a-1}+9x^{2a-4}
  1. 9x2a−25y2m\hspace{0.1cm}9x^{2a}-25y^{2m}
  2. a2x+2−4b2x−2\hspace{0.1cm}a^{2x+2}-4b^{2x-2}
  3. a6−6a4b+12a2b2−8b3\hspace{0.1cm}a^6-6a^4 b+12a^2 b^2-8b^3
  1. 8x3+36x2y+54xy2+27y3\hspace{0.1cm}8x^3+36x^2 y+54xy^2+27y^3
  2. 916a4−34a3+2920a2−45a+1625\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. 9−36a+42a2−18a3+13a4−2a5+a6\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. (x+1)(ax+a+1)\hspace{0.1cm}\left(x+1\right)\left(ax+a+1\right)
  2. (a+b)(a2−ab+b2+a−b)\hspace{0.1cm}\left(a+b\right)\left(a^2-ab+b^2+a-b\right)
  3. (y2+4)(y+2)(y−2)\hspace{0.1cm}\left(y^2+4\right)\left(y+2\right)\left(y-2\right)
  4. (2an+bn)(2an−bn)⋅(4a2n−2anbn+b2n)⋅(4a2n+2anbn+b2n)\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. (3n−5)(3n+4)\hspace{0.1cm}\left(3^n-5\right)\left(3^n+4\right)
  6. (a2+1)(1−b)\hspace{0.1cm}\left(a^2+1\right)\left(1-b\right)
  7. (t2+1)(t4+1)\hspace{0.1cm}\left(t^2+1\right)\left(t^4+1\right)
  1. (x−yn)(2x+yn)\hspace{0.1cm}\left(x-y^n\right)\left(2x+y^n\right)
  2. (x−4y+6a−b)(x−4y−6a+b)\hspace{0.1cm}\left(x-4y+6a-b\right)\left(x-4y-6a+b\right)
  3. (2x−1)(x+1)(4x2+2x+1)⋅(x2−x+1)\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. (5+x−4y)(5−x+4y)\hspace{0.1cm}\left(5+x-4y\right)\left(5-x+4y\right)
  5. (7x2+5x−3y)(7x2−5x+3y)\hspace{0.1cm}\left(7x^2+5x-3y\right)\left(7x^2-5x+3y\right)
  6. (2a+2b+x)(2b−x)\hspace{0.1cm}\left(2a+2b+x\right)\left(2b-x\right)
  7. (4x2+8x+9)(4x2−8x+9)\hspace{0.1cm}\left(4x^2+8x+9\right)\left(4x^2-8x+9\right)
  1. (x2+9x−6)(x2−9x−6)\hspace{0.1cm}\left(x^2+9x-6\right)\left(x^2-9x-6\right)
  2. (2a4−7b4+5a2b2)(2a4−7b4−5a2b2)\hspace{0.1cm}\left(2a^4-7b^4+5a^2 b^2\right)\left(2a^4-7b^4-5a^2 b^2\right)
  3. (x4+1)(x2+1)(x+1)(x−1)\hspace{0.1cm}\left(x^4+1\right)\left(x^2+1\right)\left(x+1\right)\left(x-1\right)
  4. (2x−y)(2x+y)(4x2+2xy+y2)⋅(4x2−2xy+y2)\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. (4+a2)(16−4a2+a4)\hspace{0.1cm}\left(4 +a^2\right)\left(16 -4a^2 +a^4\right)
  6. (2a+3b2)(4a2−6ab2+9b4)\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. Cocciente:  3ax+3−ax+2+ax+1  Residuo:  0\hspace{0.1cm}\text{Cocciente:}\;3a^{x+3}-a^{x+2}+a^{x+1}\\\text{\;Residuo:}\;0
  2. Cociente:  4x2+2x  Residuo: −7x+1\hspace{0.1cm}\text{Cociente:}\;4x^2+2x\\\text{\;Residuo:}\ -7x+1
  3. Cociente:  2x+2  Residuo:  −3x\hspace{0.1cm}\text{Cociente:}\;2x+2\\\text{\;Residuo:}\; -3x
  1. Cociente:  −x−1  Residuo:  −x+11\hspace{0.1cm}\text{Cociente:}\;-x-1\\\text{\;Residuo:}\; -x+11
  2. Cociente:  −2x+12  Residuo:  74x−54\hspace{0.1cm}\text{Cociente:}\;-2x+12\\\text{\;Residuo:}\;74x-54

Solución ejercicios del 41 al 45. racionalización de denominadores.

  1. x+y\hspace{0.1cm}\sqrt{x}+\sqrt{y}
  2. x23+xy3+y23x−y\hspace{0.1cm}\cfrac{\sqrt[3]{x^2}+\sqrt[3]{xy}+\sqrt[3]{y^2}}{x-y}
  3. a4−1+1\hspace{0.1cm}\sqrt{a^4-1}+1
  1. 2(ax−3a)ax−9\hspace{0.1cm}\cfrac{2\left(a\sqrt{x}-3\sqrt{a}\right)}{ax-9}
  2. x2−1+1\hspace{0.1cm}\sqrt{x^2-1}+1