11) ax²y - bx²y - ax + bx + 2a - 2b

= (ax²y - bx²y) - (ax - by) + (2a - 2b)

= x²y(a - b) - x(a - b) + 2(a - b)

= (a - b)(x²y - x + 2)

12) 3ax² + 3bx² + ax + bx + 5a + 5b

= (3ax² + 3bx²) + (ax + bx) + (5a + 5b)

= 3x²(a + b) + x(a + b) + 5(a + b)

= (a + b)(3x² + x + 5)

13) ax² - bx² - 2ax + 2bx - 3a + 3b

= (ax² - bx²) - (2ax - 2bx) - (3a - 3b)

= x²(a - b) - 2x(a - b) + 3(a - b)

= (a - b)(x² - 2x + 3)

14) 2ax² - bx² - 2ax + bx + 4a - 2b

= (2ax² - bx²) - (2ax - bx) + (4a - 2b)

= x²(2a - b) - x(2a - b) + 2(2a - b)

= (2a - b)(x² - x + 2)

15) ax² - 5x² - ax + 5x + a - 5

= (ax² - 5x²) - (ax - 5x) + (a - 5)

= x²(a - 5) - x(a - 5) + (a - 5)

= (a - 5)(x² - x + 1)

16) x² + 8x + 3x + 24 = 0

(x² + 8x) + (3x + 24) = 0

x(x + 8) + 3(x + 8) = 0

(x + 8)(x + 3) = 0

x + 8 = 0 hoặc x + 3 = 0

*) x + 8 = 0

x = -8

*) x + 3 = 0

x = -3

Vậy x = -8; x = -3

17) x² - 8x - 3x + 24 = 0

(x² - 8x) - (3x + 24) = 0

x(x - 8) - 3(x - 8) = 0

(x - 8)(x - 3) = 0

x - 8 = 0 hoặc x - 3 = 0

*) x - 8 = 0

x = 8

*) x - 3 = 0

x = 3

Vậy x = 3; x = 8

18) x² + 8x - 3x - 24 = 0

(x² + 8x) - (3x + 24) = 0

x(x + 8) - 3(x + 8) = 0

(x + 8)(x - 3) = 0

x + 8 = 0 hoặc x - 3 = 0

*) x + 8 = 0

x = -8

*) x - 3 = 0

x = 3

Vậy x = -8; x = 3

19) x² - 8x + 3x - 24 = 0

(x² - 8x) + (3x - 24) = 0

x(x - 8) + 3(x - 8) = 0

(x - 8)(x + 3) = 0

x - 8 = 0 hoặc x + 3 = 0

*) x - 8 = 0

x = 8

*) x + 3 = 0

x = -3

Vậy x = -3; x = 8

10) x² - 20x + x - 20 = 0

(x² - 20x) + (x - 20) = 0

x(x - 20) + (x - 20) = 0

(x - 20)(x + 1) = 0

x - 20 = 0 hoặc x + 1 = 0

*) x - 20 = 0

x = 20

*) x + 1 = 0

x = -1

Vậy x = -1; x = 20

11) x² + 20x - x - 20 = 0

(x² + 20x) - (x + 20) = 0

x(x + 20) - (x + 20) = 0

(x + 20)(x - 1) = 0

x + 20 = 0 hoặc x - 1 = 0

*) x + 20 = 0

x = -20

*) x - 1 = 0

x = 1

Vậy x = -20; x = 1

12) x² + 12x + 2x + 24 = 0

(x² + 12x) + (2x + 24) = 0

x(x + 12) + 2(x + 12) = 0

(x + 12)(x + 2) = 0

x + 12 = 0 hoặc x + 2 = 0

*) x + 12 = 0

x = -12

*) x + 2 = 0

x = -2

Vậy x = -12; x = -2

13) x² - 12x - 2x + 24 = 0

(x² - 12x) - (2x - 24) = 0

x(x - 12) - 2(x - 12) = 0

(x - 12)(x - 2) = 0

x - 12 = 0 hoặc x - 2 = 0

*) x - 12 = 0

x = 12

*) x - 2 = 0

x = 2

Vậy x = 2; x = 12

14) x² + 6x + 4x + 24 = 0

(x² + 6x) + (4x + 24) = 0

x(x + 6) + 4(x + 6) = 0

(x + 6)(x + 4) = 0

x + 6 = 0 hoặc x + 4 = 0

*) x + 6 = 0

x = -6

*) x + 4 = 0

x = -4

Vậy x = -6; x = -4

15) x² - 6x - 4x + 24 = 0

(x² - 6x) - (4x - 24) = 0

x(x - 6) - 4(x - 6) = 0

(x - 6)(x - 4) = 0

x - 6 = 0 hoặc x - 4 = 0

*) x - 6 = 0

x = 6

*) x - 4 = 0

x = 4

Vậy x = 4; x = 6

5) x² + 2x - 3x - 6 = 0

(x² + 2x) - (3x + 6) = 0

x(x + 2) - 3(x + 2) = 0

(x + 2)(x - 3) = 0

x + 2 = 0 hoặc x - 3 = 0

*) x + 2 = 0

x = -2

*) x - 3 = 0

x = 3

Vậy x = -2; x = 3

6) x² - 4x + 5x - 20 = 0

(x² - 4x) + (5x - 20) = 0

x(x - 4) + 5(x - 4) = 0

(x - 4)(x + 5) = 0

x - 4 = 0 hoặc x + 5 = 0

*) x - 4 = 0

x = 4

*) x + 5 = 0

x = -5

Vậy x = -5; x = 4

7) x² + 4x - 5x - 20 = 0

(x² + 4x) - (5x + 20) = 0

x(x + 4) - 5(x + 4) = 0

(x + 4)(x - 5) = 0

x + 4 = 0 hoặc x - 5 = 0

*) x + 4 = 0

x = -4

*) x - 5 = 0

x = 5

Vậy x = -4; x = 5

8) x² - 10x + 2x - 20 = 0

(x² - 10x) + (2x - 20) = 0

x(x - 10) + 2(x - 10) = 0

(x - 10)(x + 2) = 0

x - 10 = 0 hoặc x + 2 = 0

*) x - 10 = 0

x = 10

*) x + 2 = 0

x = -2

Vậy x = -2; x = 10

9) x² + 10x - 2x - 20 = 0

(x² + 10x) - (2x + 20) = 0

x(x + 10) - 2(x + 10) = 0

(x + 10)(x - 2) = 0

x + 10 = 0 hoặc x - 2 = 0

*) x + 10 = 0

x = -10

x - 2 = 0

x = 2

Vậy x = -10; x = 2

1) x² - 7x = 0

x(x - 7) = 0

x = 0 hoặc x - 7 = 0

*) x - 7 = 0

x = 7

Vậy x = 0; x = 7

2) -3x² + 5x = 0

x(-3x + 5) = 0

x = 0 hoặc -3x + 5 = 0

*) -3x + 5 = 0

-3x = -5

x = 5/3

Vậy x = 0; x = 5/3

3) x² + 3x - 2x - 6 = 0

(x² + 3x ) - (2x + 6) = 0

x(x + 3) - 2(x + 3) = 0

(x + 3)(x - 2) = 0

*) x + 3 = 0

x = -3

*) x - 2 = 0

x = 2

Vậy x = -3; x = 2

4) x² + 6x - x - 6 = 0

(x² + 6x) - (x + 6) = 0

x(x + 6) - (x + 6) = 0

(x + 6)(x - 1) = 0

*) x + 6 = 0

x = -6

*) x - 1 = 0

x = 1

Vậy x = -6; x = 1

a) 456/457 = 1 - 1/457

458/459 = 1 - 1/459

Do 457 < 459 nên 1/457 > 1/459

Do đó 1 - 1/457 < 1 - 1/459

Vậy 456/457 < 458/459

b) 27/49 < 28/49

Do 49 > 39 nên 28/49 < 28/39

Vậy 27/49 < 28/39

a mod 2 <> 0

a) 4.5.6.7.8 chia hết cho 7

6.7.8.9 chia hết cho 7

Vậy 4.5.6.7.8 + 6.7.8.9 chia hết cho 7

b) 4251 không chia hết cho 6

3030 chia hết cho 6

12 chia hết cho 6

Vậy 4251 + 3030 + 12 không chia hết cho 6

c) 121 chia hết cho 11

77 chia hết cho 11

Vậy 121 - 77 chia hết cho 11

d) 119 không chia hết cho 13

52 chia hết cho 13

Vậy 119 - 52 không chia hết cho 13

S = 1 + 4 + 7 + ... + 40

Số các số:

(40 - 1) : 3 + 1 = 14 số

S = (40 + 1) . 14 : 2

= 41 . 7

= 287