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# 6.5E: Ejercicios

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## La práctica hace a la perfección

Reconocer y utilizar el método apropiado para factorizar un polinomio completamente

En los siguientes ejercicios, factor completamente.

1. $$2n^2+13n−7$$

Contestar

$$(2n−1)(n+7)$$

2. $$8x^2−9x−3$$

3. $$a^5+9a^3$$

Contestar

$$a^3(a^2+9)$$

4. $$75m^3+12m$$

5. $$121r^2−s^2$$

Contestar

$$(11r−s)(11r+s)$$

6. $$49b^2−36a^2$$

7. $$8m^2−32$$

Contestar

$$8(m−2)(m+2)$$

8. $$36q^2−100$$

9. $$25w^2−60w+36$$

Contestar

$$(5w−6)^2$$

10. $$49b^2−112b+64$$

11. $$m^2+14mn+49n^2$$

Contestar

$$(m+7n)^2$$

12. $$64x^2+16xy+y^2$$

13. $$7b^2+7b−42$$

Contestar

$$7(b+3)(b−2)$$

14. $$30n^2+30n+72$$

15. $$3x^4y−81xy$$

Contestar

$$3xy(x−3)(x^2+3x+9)$$

16. $$4x^5y−32x^2y$$

17. $$k^4−16$$

Contestar

$$(k−2)(k+2)(k^2+4)$$

18. $$m^4−81$$

19. $$5x5y^2−80xy^2$$

Contestar

$$5xy^2(x^2+4)(x+2)(x−2)$$

20. $$48x^5y^2−243xy^2$$

21. $$15pq−15p+12q−12$$

Contestar

$$3(5p+4)(q−1)$$

22. $$12ab−6a+10b−5$$

23. $$4x^2+40x+84$$

Contestar

$$4(x+3)(x+7)$$

24. $$5q^2−15q−90$$

25. $$4u^5v+4u^2v^3$$

Contestar

$$u^2(u+1)(u^2−u+1)$$

26. $$5m^4n+320mn^4$$

27. $$4c^2+20cd+81d^2$$

Contestar

prime

28. $$25x^2+35xy+49y^2$$

29. $$10m^4−6250$$

Contestar

$$10(m−5)(m+5)(m^2+25)$$

30. $$3v^4−768$$

31. $$36x^2y+15xy−6y$$

Contestar

$$3y(3x+2)(4x−1)$$

32. $$60x^2y−75xy+30y$$

33. $$8x^3−27y^3$$

Contestar

$$(2x−3y)(4x^2+6xy+9y^2)$$

34. $$64x^3+125y^3$$

35. $$y^6−1$$

Contestar

$$(y+1)(y−1)(y^2−y+1)$$

36. $$y^6+1$$

37. $$9x^2−6xy+y^2−49$$

Responder

$$(3x−y+7)(3x−y−7)$$

38. $$16x^2−24xy+9y^2−64$$

39. $$(3x+1)^2−6(3x−1)+9$$

Responder

$$(3x−2)2$$

40. $$(4x−5)^2−7(4x−5)+12$$

## Ejercicios de escritura

41. Explica lo que significa factorizar un polinomio por completo.

Responder

Las respuestas variarán.

42. La diferencia de cuadrados se $$y^4−625$$ puede factorizar como $$(y^2−25)(y^2+25)$$. Pero no se tiene en cuenta del todo. Qué más hay que hacer para factorizar completamente.

43. De todos los métodos de factoring cubiertos en este capítulo (GCF, agrupación, deshacer FOILO, método 'ac', productos especiales) ¿cuál es el más fácil para usted? ¿Cuál es el más difícil? Explica tus respuestas.

Responder

Las respuestas variarán.

44. Crea tres problemas de factoring que serían buenas preguntas de prueba para medir tus conocimientos de factoring. Mostrar las soluciones.

## Autocomprobación

a. Después de completar los ejercicios, utilice esta lista de verificación para evaluar su dominio de los objetivos de esta sección.

b. En una escala de 1-10, ¿cómo calificaría su dominio de esta sección a la luz de sus respuestas en la lista de verificación? ¿Cómo se puede mejorar esto?

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