factor completlly?

Question

1: Factor each completely:
x2 - 64

(x - 8)2
(x - 16)(x - 4)
(x + 8)(x - 8)


2: x2 + 4x + 4
(x + 2)2
(x + 4)(x + 1)
(x - 2)(x + 2)


3: 25x2 - 30x + 9
(5x - 3)2
5(x + 3)(x - 3)
(5x + 3)(5x - 3)


4: 4x2 - 144
4(x - 6)2
4(x - 6)( x + 6)
(4x - 12)(x + 12)


5: 36x2 - 12x + 1
(6x - 1)2
(6x - 1)(6x + 1)
(6x - 4)(6x + 3)


6: 6b2c3 - 18b2c2d2
6bc (c - 3d)
6b2c2d2(c - 3)
6b2c2(c - 3d2)


7: 4x4 + 40x3
(4x2 + x)(10x2 + x2)
4x3(x + 10)
(4x2 + x)2


8: x2 - 6x + 9
(x - 3)(x + 3)
(x - 3)2
(x - 2)(x - 4)


9: x2 - 121
(x - 11)(x + 11)
(x - 11)2
(x + 11)2


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


11: x2 - 22x + 121
(x - 11)2
(x - 11)(x + 11)
(x + 11)2


12: 49x2 - 64
(7x - 8)(7x + 8)
7(x2 - 9)
7(x - 3)(x + 3)


13: 16x2 - 25
(4x + 5) (4x - 5)
(4x - 5)2
(4x + 5)2


14: 49x2 - 100
(7x +10)2
(7x - 10)2
(7x + 10) (7x - 10)


15: 9x2 + 48x + 64
(3x + 8)2
(3x - 8)2
(3x + 8)(3x - 8)


16: 6x2 - 60x + 150
6(x + 5)2
6(x - 5)2
(6x - 5)2


17: 7x2 - 63
7(x + 3)(x - 3)
7(x + 3)2
7(x - 3)2


18: Solve these by factoring:
2r2 - 162 = 0

r = 0, -9, 9
r = -9, 9
r = 2, -9, 9


19: 3x3 - 3x = 0
x = 1
x = -1, 1
x = -1, 0, 1


20: 81x2 + 200x + 100 - 20x = 0
x = -9, -10
x = -10/9
x = 0, 9, 10

Answer 1

Hi,

1: Factor each completely:
x2 - 64
(x + 8)(x - 8)

2: x2 + 4x + 4
(x + 2)2

3: 25x2 - 30x + 9
(5x - 3)2

4: 4x2 - 144
4(x - 6)( x + 6)

5: 36x2 - 12x + 1
(6x - 1)2

6: 6b2c3 - 18b2c2d2
6b2c2(c - 3d2)

7: 4x4 + 40x3
4x3(x + 10)

8: x2 - 6x + 9
(x - 3)2

9: x2 - 121
(x - 11)(x + 11)

10: x2 + 8x + 16
(x + 4)2

11: x2 - 22x + 121
(x - 11)2

12: 49x2 - 64
(7x - 8)(7x + 8)

13: 16x2 - 25
(4x + 5) (4x - 5)

14: 49x2 - 100
(7x + 10) (7x - 10)

15: 9x2 + 48x + 64
(3x + 8)2

16: 6x2 - 60x + 150
6(x - 5)2

17: 7x2 - 63
7(x + 3)(x - 3)

18: Solve these by factoring:
2r2 - 162 = 0
r = -9, 9

19: 3x3 - 3x = 0
x = -1, 0, 1

20: 81x2 + 200x + 100 - 20x = 0
x = -10/9


I hope that helps!! :-)

Answer 2

For the first several questions, note that when we have
(ax + b) (cx + d) = ex^2 + fx + g
(with a, c > 0), then the following are true:
- g positive and f positive means b and d are both positive
- g positive and f negative means b and d are both negative
- g negative means that one of b and d is positive and the other negative.

1: x^2 - 64
= x^2 - 8^2, difference of perfect squares
= (x-8) (x+8)

2: x^2 + 4x + 4
= (x + 2)^2 - in general x^2 + 2ax + a^2 = (x+a)^2

3: 25x^2 - 30x + 9
= (5x - 3)^2

4: 4x^2 - 144
= 4(x - 6)( x + 6)

5: 36x^2 - 12x + 1
= (6x - 1)^2

6: 6b^2c^3 - 18b^2c^2d^2: here we just take out the common factor
= 6b^2c^2 (c - 3d^2)

7: 4x^4 + 40x^3: again just take out the common factor
= 4x^3(x + 10)

8: x^2 - 6x + 9
= (x - 3)^2

9: x^2 - 121
= (x - 11)(x + 11)

10: x^2 + 8x + 16
= (x + 4)^2

11: x^2 - 22x + 121
= (x - 11)^2

12: 49x^2 - 64 = (7x)^2 - 8^2
= (7x - 8)(7x + 8)

13: 16x^2 - 25 = (4x)^2 - 5^2
= (4x + 5) (4x - 5)

14: 49x^2 - 100 = (7x)^2 - 10^2
= (7x + 10) (7x - 10)

15: 9x^2 + 48x + 64
= (3x + 8)^2

16: 6x^2 - 60x + 150 = 6 (x^2 - 10x + 25)
= 6(x - 5)^2

17: 7x^2 - 63
= 7(x + 3)(x - 3)

18: Solve these by factoring:
2r^2 - 162 = 0
<=> 2(r^2 - 81) = 0
<=> 2(r-9)(r+9) = 0
<=> 2 = 0 or (r-9) = 0 or (r+9) = 0
<=> r = 9 or r = -9.

19: 3x^3 - 3x = 0
<=> 3x (x^2 - 1) = 0
<=> 3x (x-1) (x+1) = 0
<=> 3x = 0 or (x-1) = 0 or (x+1) = 0
<=> x = 0, 1 or -1.

20: 81x2 + 200x + 100 - 20x = 0
<=> 81x^2 + 180x + 100 = 0
<=> (9x + 10)^2 = 0
<=> 9x + 10 = 0
<=> x = -10/9.

Answer 3

x² - 64 = (x-8)(x+8)
<>
2: x² + 4x + 4 = (x + 2)(x + 2)
<>
3: 25x² - 30x + 9 = (5x + 3)(5x - 3)
<>
4: 4x² - 144 = 4(x - 6)( x + 6) or (2x - 12)(2x + 12)
><
5: 36x² - 12x + 1= (6x - 1)(6x - 1) = (6x - 1)²
><
6: 6b²c³ - 18b²c²d² = 6b²c²(c - 3d²)
><
7: 4x^4 + 40x³ =
4x³(x + 10)
><
8: x² - 6x + 9
(x - 3)(x - 3)
><
9: x² - 121 = (x - 11)(x + 11)
><
10: x + 8x + 16 = (x + 4)(x + 4) = (x + 4)²
><
11: x² - 22x + 121 = (x - 11)² = (x - 11)(x - 11)
><
12: 49x² - 64
(7x - 8)(7x + 8)
><
13: 16x² - 25
(4x + 5) (4x - 5)
><
14: 49x² - 100 = (7x + 10) (7x - 10)
><
15: 9x² + 48x + 64 = (3x + 8)² = (3x +8)(3x + 8)
<>
16: 6x² - 60x + 150 =
6(x² - 10x + 25) = 6(x - 5)(x - 5) = 6(x + 5)²
><
17: 7x² - 63
><
18: Solve these by factoring:
2r² - 162 = 0
2(r² - 81) = 2(r + 9)(r - 9)
r = -9, 9
><
19: 3x³ - 3x = 0
3x(x² - 1)= 3x(x+1)(x - 1)
x = -1, 0, 1
><
20: 81x² + 200x + 100 - 20x = 0
(9x +10)(9x + 10) = (9x + 10)²
x = -10/9
><

Answer 4

1) x^2 - 64 = x^2 - (8)^2
= (x + 8)(x - 8)

2) x^2 + 4x +4 = (x + 2)(x + 2)
= (x + 2)^2

3) 25x^2 - 30x + 9 = (5x - 3)(5x - 3)
= (5x - 3)^2

4) 4x^2 - 144 = 4(x^2 - 36)
= 4(x^2 - 6^2)
= 4(x - 6)(x + 6)

5) 36x^2 -12x + 1 = (6x - 1)(6x - 1)
= (6x - 1)^2

6) 6b^2c^2 - 18b^2c^2d^2 = 6b^2c^2(1 - 3d^2)
= 6b^2c^2(1 - 3d)(1 + 3d)

7) 4x^4 + 40x^3 = 4x^3(x + 10)

8) x^2 - 6x + 9 = (x - 3)^2

9) x^2 - 121 = (x - 11)(x + 11)

10) x^2 + 8x + 16 = (x + 4)^2

11) x^2 - 22x +121 = (x - 11)^2

12) 49x^2 - 64 = (7x - 8)(7x + 8)

13) 16x^2 - 25 = (4x - 5)(4x + 5)

14) 49x^2 - 100 = (7x -10)(7x + 10)

15) 9x^2 + 48x + 64 = (3x + 8)^2

16) 6x^2 - 60x + 150 = 6(x^2 - 10x + 25)
= 6(x - 5)^2

17) 7x^2 - 63 = 7(x^2 - 9)
= 7(x - 3)(x + 3)

18) 2r^2 - 162 = 0
2(r^2 - 81) = 0
2(r - 9)(r + 9) = 0
let r - 9 = 0
r = 9
let r + 9 = 0
r = - 9

therefore the value of x are - 9 or 9

19) 3x^3 - 3x = 0
3x(x^2 - 1) = 0
3x(x - 1)(x + 1) = 0
let 3x = 0
x = 0

let x - 1 = 0
x = 1

let x + 1 = 0
x = -1
therefore the value of x are 0 , -1 or 1.

20) 81x^2 + 200x + 100 - 20x = 0
81x^2 +180x +100 = 0
(9x + 10)^2 = 0
let 9x + 10 = 0
x = - 10/9
therefore the value of x is -10/9

Answer 5

1. x2 - 64=(x-8)(x+8)
2. x2 + 4x + 4=(x+2)^2
3. 25x2 - 30x + 9=(5x-3)^2
4. 4x2 - 144=4(x-6)(x+6)
5. 36x2 - 12x + 1=(6x-1)^2
6. 6b2c3 - 18b2c2d2=6b^2c^2(c-3d^2)
7. 4x4 + 40x3=4x^3(x+10)
8. x2 - 6x + 9=(x-3)^2
9. x2 - 121=(x-11)(x+11)
10. x2 + 8x + 16=(x+4)^2
11. x2 - 22x + 121=(x-11)^2
12. 49x2 - 64=(7x-8)(7x+8)
13. 16x2 - 25=(4x-5)(4x+5)
14. 49x2 - 100=(7x-10)(7x+10)
15. 9x2 + 48x + 64= (3x+8)^2
16. 6x2 - 60x + 150=6(x-5)^2
17. 7x2 - 63=7(x-3)(x+3)
18. 2r2 - 162 = 0 ->2(r^2-81)=0 -> 2(r-9)(r+9)=0 -> r=9 or -9
19. 3x3 - 3x = 0 -> 3x(x^2-1)=0 -> 3x(x-1)(x+1)=0 -> x=0,1,or -1
20. 81x2 + 200x + 100 - 20x = 0 ->81x^2+180x+100=0 ->(9x+10)^2=0 -> x=-10/9

Answer 6

1;(x+8)(x-8)
2;(x+2)2
3;(5x-3)2
4;4(x - 6)( x + 6)
5: (6x - 1)2
6: 6b2c2(c - 3d2)
7: 4x3(x + 10)
8: (x - 3)2
9: (x - 11)(x + 11)
10: (x + 4)2
11: (x - 11)2
12: (7x - 8)(7x + 8)
13: (4x + 5) (4x - 5)
14: (7x + 10) (7x - 10)
15: (3x + 8)2
16: 6(x - 5)2
17: 7(x + 3)(x - 3)
18:r = -9, 9
19: x = -1, 0, 1
20:x = -10/9

Answer 7

1;(x+8)(x-8)
2;(x+2)2
3;(5x-3)2
4;4(x - 6)( x + 6)
5: (6x - 1)2
6: 6b2c2(c - 3d2)
7: 4x3(x + 10)
8: (x - 3)2
9: (x - 11)(x + 11)
10: (x + 4)2
11: (x - 11)2
12: (7x - 8)(7x + 8)
13: (4x + 5) (4x - 5)
14: (7x + 10) (7x - 10)
15: (3x + 8)2
16: 6(x - 5)2
17: 7(x + 3)(x - 3)
18:r = -9, 9
19: x = -1, 0, 1
20:x = -10/9

Answer 8

i do not like the show or any show that treats people the way they do and break the hearts of people the way they do and remember SIMON COWELL & CO HAVE MADE MILLIONS OUT OF THIS and the heartbreak they cause they should be banned so i agree with you X FACTOR X FACTOR X fACTOR!!!!??? Is that enough X Factor now?? Can we stop going on about it, please???xx STOP THESE PROGRAMMES ALTOGETHER PUT THE YALIBAN in charge they will soon have them stopped

Answer 9

In the time it took you to type all of that, you could have learned how to factor and done it yourself. That's just lazy.