SOLUTION: Please help me, I'm so lost! :'( 1. 125x3 + 64 A (5x - 4)(25x2 + 20x - 16) B(5x + 16)(25x2 - 20x + 2) C(5x + 8)(25x2 - 40x + 16) D(5x + 4)(25x2 - 20x + 16) E (5x + 2)

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Question 766739: Please help me, I'm so lost! :'(
1. 125x3 + 64
A (5x - 4)(25x2 + 20x - 16)
B(5x + 16)(25x2 - 20x + 2)
C(5x + 8)(25x2 - 40x + 16)
D(5x + 4)(25x2 - 20x + 16)
E (5x + 2)(25x2 - 40x + 16)
F cannot be factored

2. 216a3 + 1
A (3a + 1)(24a2 - 8a + 1)
B(6a + 1)(36a2 - 6a + 1)
C(18a + 1)(2a2 - 6a + 1)
D(4a + 1)(20a2 - 4a + 1)
E (6a - 1)(36a2 + 6a + 1)
F cannot be factored

3. 7x5 - 64y
A 7xy(x2 - 8)(x2 + 8)
B7x(x2 - 8)(x2 + 7)
C7xy(x4 - 8)
D7x(x2 - 9)(x2 + 1)
E 7(x5 - 9x)
F cannot be factored

4. 27x3 - 8
A (3x - 2)(3x + 2)2
B(3x - 2)(9x2 - 6x + 4)
C(3x + 2)(3x2 - 3x - 4)
D(27x + 2)(x2 - 2x + 4)
E (3x - 2)(9x2 + 6x + 4)
F cannot be factored

5. x9 + 1
A (x + 1)(x2 - x + 1)(x6 - x3 + 1)
B(x3 + 1)(x6 + 1)
C(x + 1)(x2 - x + 1)(x3-1)2
D(x + 1)3(x2 - x + 1)3
E (x3 + 1)(x6 - x3 + 1)
F cannot be factored


6. 2x8 - 26x4 + 13
A (2x4 - 7)(x4 + 3)
B2(x4 + 7)(x4 + 3)
C2(x4 - 13)(x4 - 1)
D2(x4 + 13/2)(x4 + 13/2)
E 2(x4 + 13/4) (x4 + 13/4)
F cannot be factored

7. a3 - 64
A (a - 4)(a2 + 4a + 16)
B(a + 4)(a2 + 16)
C(a + 4)(a2 + 4a + 16)
D(a - 4)(a2 + 4a - 16)
E (a2 + 4a - 4)(a + 4)
F cannot be factored

8. a4 - 64
A (a - 2)(a - 4)(a2 - 8)
B(a2 - 8)(a2 + 8)
C(a + 2)(a - 4)(a2 + 8)
D(a - 2)(a + 4)(a2 + 8)
E (a2 - 16)(a2 + 4)
F cannot be factored

9. 2m4 - 2mn3
A 2m(m2 + mn + n2)
B2mn(m2 + mn + n2)
C3m(m2 + mn + n2)
D2m(m - n)(m2 + mn + n2)
E 2m(m - n)(m + n)
F cannot be factored

10. 2x9 + 16
A 2(x - 2)(x8 - 2x4 + 4)
B2(x3 - 2)(x6 - 2x3 + 2)
C(2x3 + 2)(x6 - 2x3 - 4)
D2(x3 + 2)(x6 - 2x3 + 4)
E 2x3(x6 + 2x3 + 4)
F cannot be factored

11. x4 + 2x3 - 8x - 16
A (x + 2)(x2 + 2x + 4)
B(x - 2)(x2 + 2x + 4)
C(x - 2)(x + 2)(x2 + 2x + 4)
D(x + 2)(x2 + 4x + 8)
E (x2 + 4x - 4)(x2 + 2x + 4)
F cannot be factored

12. x3 - 12x2 + 48x - 64
A (x - 4)(x + 4)2
B(x-4)3
C(x + 4)3
D(x + 4)(x - 4)2
E (x - 4)(x2 + 2x + 1)
F cannot be factored

13. -2w4 + 1250
A -2(w2 + 25)
B(w - 5)(w + 5)(w2 + 25)
C-2(w - 5)(w2 + 25)
D-2(w - 5)(w - 5)(w2 + 25)
E -2(w - 5)(w + 5)(w2 + 25)
F cannot be factored

14. a9 - 1
A (a3 - 1)(a6 + a3 + 1)
B(a + 1)(a6 + a3 + 1)
C(a - 1)(a2 - a - 1)(a6 + a3 + 1)
D(a - 1)(a2 + a + 1)(a6 + a3 + 1)
E (a3 + a + 1)(a6 + a3 + 1)
F cannot be factored

15. a4 + 3a3+ 27a + 81
A (a2 + 3a - 9)(a2 + 2a + 3)
B(a - 3)(a2 + 3a + 9)
C(a + 3)(a2 + 2a + 3)
D(a + 3)(a2 + 4a + 9)
E [(a + 3)2](a2 - 3a + 9)
F cannot be factored

16. x8 - 16x4
A x4(x - 2)(x + 2)(x2 + 4)
B(x4 + 4x2)2
C(x4 - 4x2)2
D(x4 + 4x2)(x4 - 4x2)
E x4(x4 - 16)
F cannot be factored

17. a4 + 1
A (a2 + 1)2
B(a2 - 1)(a2 - 1)
Ca2(a2 + 1)
D(a2 + 1)(a2 - 1)
E a2 (a + 1)2
F cannot be factored

18. 3a4 + 81a
A (a + 3)(a2 + 3a + 9)
B(3a2 + 3)(a2 - 3a + 9)
C(a2 + 3a)(a2 - 3a + 9)
D3a(a + 3)(a2 - 3a + 9)
E (3a + 3)(a2 + 3a - 9)
F cannot be factored

19. x3 + x2 - x - 1
A (x - 1)(x2 + 2x + 1)
B(x + 1)4
C(x2 + 1)2
D(x + 1)3
E (x - 1)(x + 1)2
F cannot be factored

Answer by ramkikk66(644)   (Show Source): You can put this solution on YOUR website!
Hi,

Most of your problems can be solved using the following 3 identities:
1) 
2) 
3) 

I'm solving a few below - go through these and try the rest yourself.

1) 
=      => Now it is of the form a^3 + b^3

=   --> Using identity (2)

Choice D

2) 

=  => Now it is of the form a^3 - b^3
=   ---> Using identity (1)

Choice E

3) 

=  => Now it is of the form a^2 - b^2
=     ---> Using identity (3)
Choice B

4)
  ---> take out the common factor of -2
= 
=  => Now it is of the form a^2 - b^2
=     ---> Using identity (3)
=    ---> since w^2 - 25 is also of the form a^2 - b^2
Choice E

Hope you get the idea now :)




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