factoring ..?

Question

Factor completly?
1: Factor.
3x2 - 192

(x - 8)(x + 8)
3(x+ 8)(x + 8)
3(x - 8)(x + 8)


2: 162x2 - 8
2(9x - 2)(9x + 2)
2(9x - 2)(9x - 2)
(9x - 2)(9x + 2)


3: 2x2 - 28x + 48
2(x - 4)(x - 6)
2(x - 2)(x - 12)
(x - 2)(x - 12)


4: 3x2 - 30x + 63
(x - 21)(x - 3)
3(x + 7)(x - 3)
3(x - 7)(x - 3)


5: 16x2 - 8x + 1
(4x - 1)(4x - 1)
(8x - 1)(2x - 1)
(16x - 1)(x - 1)


6: 3x2 - 42x + 72
(3x - 12)(x - 2)
3(x - 12)(x - 2)
(x - 12)(x - 2)


7: 4x2 + 8x - 320
(4x - 8)(x + 10)
4(x - 8)(x + 10)
4(x - 16)(x + 5)


8: 2x2 + 10x + 12
2(x + 2)(x + 3)
(x + 3)(2x - 4)
(2x + 3)(x + 4)


9: 9x2 - 3x + 18x - 6
(x + 2)(3x - 1)
(3x + 2)(3x - 1)
3(x + 2)(3x - 1)


10: 2x3 - 2x + 3x2 - 3
(x - 1)(2x - 3)
2(x + 1)(x - 1)(x + 3)
(x + 1)(x - 1)(2x + 3)


11: 3x3 + 3x2 - 27x - 27
3(x - 9)(x - 3)
3(x + 1)(x + 3)(x - 3)
(x + 1)(x + 3)(x - 3)


12: (x4 - 16)
(X - 2)(X + 2)(X2 + 4)
(X - 2)(X + 2)(X + 4)
(X - 2)(X + 2)(X2 + 2)


13: (Y4 - 81)
(Y - 3)(Y + 3)(Y2 + 9)
(Y - 3)(Y + 3)(Y + 9)
(Y - 3)(Y + 3)(Y2 + 3)


14: 8x2 - 18
(2x + 3)(2x - 3)
2(2x + 3)(2x - 3)
2(2x + 3)(x - 3)


15: 2x2 - 16x + 32
(x - 4)(x - 4)
(2x - 4)(x - 4)
2(x - 4)(x - 4)

Answer 1

1: 3x² - 192 = 3(x² - 64) = 3(x² - 8²) = 3(x-8)(x+8)
[use the formula (a² - b²) = (a-b)(a+b)]

2: 162x² - 8 = 2(81x² - 4) = 2([9x]² - 2²) = 2(9x - 2)(9x + 2)

3: 2x² - 28x + 48 = 2(x² - 14x + 24) = 2(x - 2)(x - 12)

4: 3x² - 30x + 63 = 3(x² - 10x + 21) = 3(x - 7)(x - 3)

5: 16x² - 8x + 1 = (4x - 1)² = (4x - 1)(4x - 1)

6: 3x2 - 42x + 72 = 3(x² - 14 + 24) = 3(x - 12)(x - 2)

7: 4x² + 8x - 320 = 4(x² + 2x - 80) = 4(x - 8)(x + 10)

8: 2x² + 10x + 12 = 2(x² + 5x + 6) = 2(x + 2)(x + 3)

9: 9x² - 3x + 18x - 6 = 9x² + 15x - 6 = 3(x² + 5x - 2) = 3(x + 2)(3x - 1)

10: 2x³ - 2x + 3x² - 3 = 2x(x² - 1) + 3(x² - 1) = (x² - 1)(3x + 3) =
(x + 1)(x - 1)(2x + 3)

11: 3x³ + 3x² - 27x - 27 = 3x³ - 27x + 3x² - 27 = 3x(x² - 9) + 3(x² - 9) = 3(x+1)(x² - 9) = 3(x + 1)(x + 3)(x - 3)

12: (x^4 - 16) = ([x²]² - 4²) = (x² - 4)(x² + 4) = (x - 2)(x + 2)(x² + 4)

13: (Y^4 - 81) = ([Y²]² - 9²) = (Y² - 9)(Y² +9) = (Y - 3)(Y + 3)(Y² + 9)

14: 8x² - 18 = 2(4x² - 9) = 2([2x]² - 3²) = 2(2x + 3)(2x - 3)

15: 2x² - 16x + 32 = 2(x² - 8x + 16) = 2(x - 4)² = 2(x - 4)(x - 4)

Hope this helps...

Answer 2

1. 3(x-8)(x+8)
2. 2(9x+2)(9x-2)
3.3(x-2)(x-12)
4. 3(x-7)(x-3)
5.(4x-1)(4x-1)
6.3(x-12)(x-2)
7.4(x-8)(x+10)
8. 2(x+2)(x+3)
9. 3(x+2)(x-1)
10. (x+1)(x-1)(2x+3)
11.3(x+1)(x+3)(x-3)
12. (x-2)(x+2)(x^2+4)
13. (y-3)(y+3)(y^2+9)
14. 2(2x+3)(2x-3)
15. 2(x-4)(x-4)

Answer 3

3x² - 192 -

3(x² - 64) =

3(x - 8)(x + 8)

- - - - - - - - - - -

162x² - 8 =

2(81x² - 4) =

2(9x - 2)(9x + 2)

- - - - - - - -

2x² - 28x + 28

2(x² - 14x + 24)

2(x² - 12x - 2x + 24

2[x(x - 12) - 2(x - 12)

2(x - 2)(x - 12)

- - - - - - - - - -s-