1)

a) 2x + 5 = 3⁴ : 3²

2x + 5 = 3²

2x + 5 = 9

2x = 9 - 5

2x = 4

x = 4 : 2

x = 2

b) (3x - 24).73 = 2.74

(3x - 24).73 = 148

3x - 24 = 148/73

3x = 148/73 + 24

3x = 1900/73

x = 1900/73 : 3

x = 1900/219

c) [3.(42 - x)] + 15 = 23.3

126 - 3x + 15 = 69

141 - 3x = 69

3x = 141 - 69

3x = 72

x = 72 : 3

x = 24

d) 126 + (132 - x) = 300

132 - x = 300 - 126

132 - x = 174

x = 132 - 174

x = -42

2)

a) 120 - (x + 55) = 60

x + 55 = 120 - 60

x + 155 = 60

x = 60 - 55

x = 5

b) (7x - 11).3 = 25.52 + 200

(7x - 11).3 = 1500

7x - 11 = 1500 : 3

7x - 11 = 500

7x = 500 + 11

7x = 511

x = 511 : 7

x = 73

c) 2x + 2x + 4 = 544

4x = 544 - 4

4x = 540

x = 540 : 4

x = 135

3) 

a) 10 + 2x = 49 : 47

10 + 2x = 49/47

2x = 49/47 - 10

2x = -421/47

x = -421/47 : 2

x = -421/94

b) 70 - 5(x - 3) = 45

5(x - 3) = 70 - 45

5(x - 3) = 25

x - 3 = 25 : 5

x - 3 = 5

x = 5 + 3

x = 8

c) 4 + 95 : x = 143 : 142 - 23

4 + 95 : x = -3123/142

95 : x = -3123/142 - 4

95 : x = -3691/142

x = 95 : (-3691/142)

x = -13490/3691

c: \(x^3-8x^2+x+42\)

\(=x^3+2x^2-10x^2-20x+21x+42\)

\(=\left(x+2\right)\left(x^2-10x+21\right)\)

\(=\left(x+2\right)\left(x-3\right)\left(x-7\right)\)

a: \(x^3+6x^2+11x+6\)

\(=x^3+3x^2+3x^2+9x+2x+6\)

\(=\left(x+3\right)\left(x^2+3x+2\right)\)

\(=\left(x+3\right)\left(x+1\right)\left(x+2\right)\)

Lời giải:
a.

$21\times 23-3\times 7\times (-17)$

$=21\times 23-21\times (-17)$

$=21\times 23+21\times 17=21\times (23+17)=21\times 40$

$=840$

b.

$42\times 3-7\times [(-34)+18]$

$=7\times 18-7\times (-16)$

$=7\times 18+7\times 16=7\times (18+16)=7\times 34=238$

c.

$=142\times 32+32\times (-7)-13\times 32$

$=32\times (142-7-32)=32\times 103=3296$

d.

$=13\times [(23-17)-(23+17)]$

$=13\times (23-17-23-17)=13\times (-34)=-442$

a)   x + 118 = 218

x = 218 – 118

x = 100

b)   18 – x = -17

X = 18 – (-17)

X = 35

c)    (-18) – x = -17

X = (-18) – (-17)

X = -1

d)124 + (118 – x) = 217

118 – x = 93

X = 118 – 93

X = 25

e) (3x – 6).3 = 3⁴

(3x – 6).3 = 81

3x – 6 = 27

3x = 33

ð X = 11

g) 23.(42 – x) = 46

42 – x = 2

ð X = 40

h) 84 – (3x + 8) = 34

3x + 8 = 84 – 34

3x + 8 = 50

3x = 50 – 8

3x = 42

X = 42 : 3

ð X = 14

i)               3.(2x + 1) – 19 = 14

3.(2x + 1) = 14 + 19

3.(2x + 1) = 33

2x + 1 = 33 : 3

2x + 1 = 11

2x = 11 – 1

2x = 10

X = 10 : 2

ð X = 5

k) 6x – 302 = 2³.5

6x – 302 = 40

6x = 40 + 302

6x = 342

X = 342 : 6

ð X = 57

m) (x – 1)² = 81

(x – 1)² = 9²

ð X – 1 = 9

ð X = 9 + 1

ð X = 10

n) 2^x+1 – 5 = 27

2^x+1 = 27 + 5

2^x+1 = 32

2^x+1 = 2⁵

ð X = 4

a) \(x+118=218\)

    \(x=218-118\)

    \(x=100\) 

b)\(18-x=-17\)

   \(-x=-18-17\)

    \(-x=-35\)

     \(x=35\)

c)\(\left(-18\right)-x=-17\)

     \(-x=18-17\)

     \(-x=1\)

      \(x=-1\)

d)\(124+\left(118-x\right)=217\)

    \(118-x=217-124\)

     \(118-x=93\)

     \(x=25\)

e) \(\left(3x-6\right).3=3^4\)

     \(3x-6=3^3\)

     \(3x-6=27\)

     \(x=11\)

g)\(23.\left(42-x\right)=46\)

    \(42-x=2\)

     \(x=40\)

h) \(84-\left(3x+8\right)=34\)

    \(3x+8=50\)

     \(x=14\)

 i)  \(3\left(2x+1\right)-19=14\)

      \(3\left(2x+1\right)=33\)

       \(2x+1=11\)  

        \(x=5\)

k) \(6x-302=2^3.5\)

    \(6x-302=8.5\)

    \(x=57\)

m) \(\left(x-1\right)^2=81\)

      \(\left(x-1\right)^2=9^2\)

       \(x-1=9\)

       \(x=10\)

n) \(2^{x+1}-5=27\)

    \(2^{x+1}=32\)

    \(2^{x+1}=2^5\)

   \(x+1=5\)  

     \(x=4\)

m) \(2^x+2^{x+1}+2^{x+2}=56\)

    \(2^x.1+2^x.2+2^x.2^2=56\)

    \(2^x\left(1+2+4\right)=56\)

     \(2^x=8\)

    \(2^x=2^3\)

     \(x=3\)

   \(2^x=8\)

a) \(\dfrac{27}{2}\cdot7,5+\dfrac{27}{2}\cdot2,5-150\)

\(=\dfrac{27}{2}\cdot\left(7,5+2,5\right)-150\)

\(=\dfrac{27}{2}\cdot10-150\)

\(=135-150\)

\(=-15\)

b) \(3^3\cdot\dfrac{18}{5}-3^3\cdot2\dfrac{2}{5}-3^3\cdot\dfrac{6}{5}\)

\(=3^3\cdot\dfrac{18}{5}-3^3\cdot\dfrac{12}{5}-3^3\cdot\dfrac{6}{5}\)

\(=3^3\cdot\left(\dfrac{18}{5}-\dfrac{12}{5}-\dfrac{6}{5}\right)\)

\(=3^3\cdot\left(\dfrac{18}{5}-\dfrac{18}{5}\right)\)

\(=3^3\cdot0\)

\(=0\)

a)(x + 4) - 32 = 23

   x + 4 = 23 + 32 = 55

   x = 55 - 4 = 51

b) 150 - 3x = 60 

    3x = 150 - 60 = 90 

    x = 90 : 3 = 30

c) 7x + 2x - 10 = 80 

    9x = 80 + 10 = 90

    x = 90 : 9 = 10

d) 300 - 2(x - 3) = 100

    2x - 2 * 3 = 300 - 100 = 200

    2x - 6 = 200

    2x = 200 + 6 = 206

    x = 206 : 2 = 103

a) Ta có: \(x^4+3x^3-7x^2-27x-18\)

\(=x^4-3x^3+6x^3-18x^2+11x^2-33x+6x-18\)

\(=x^3\left(x-3\right)+6x^2\left(x-3\right)+11x\left(x-3\right)+6\left(x-3\right)\)

\(=\left(x-3\right)\left(x^3+6x^2+11x+6\right)\)

\(=\left(x-3\right)\left(x^3+x^2+5x^2+5x+6x+6\right)\)

\(=\left(x-3\right)\left[x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\right]\)

\(=\left(x-3\right)\left(x+1\right)\left(x^2+5x+6\right)\)

\(=\left(x-3\right)\left(x+1\right)\left(x+2\right)\left(x+3\right)\)

b) Ta có: \(x^3-8x^2+x+42\)

\(=x^3-7x^2-x^2+7x-6x+42\)

\(=x^2\left(x-7\right)-x\left(x-7\right)-6\left(x-7\right)\)

\(=\left(x-7\right)\left(x^2-x-6\right)\)

\(=\left(x-7\right)\left(x-3\right)\left(x+2\right)\)

c) Ta có: \(x^4+5x^3-7x^2-41x-30\)

\(=x^4+5x^3-7x^2-35x-6x-30\)

\(=x^3\left(x+5\right)-7x\left(x+5\right)-6\left(x+5\right)\)

\(=\left(x+5\right)\left(x^3-7x-6\right)\)

\(=\left(x+5\right)\left(x^3-x-6x-6\right)\)

\(=\left(x+5\right)\left[x\left(x^2-1\right)-6\left(x+1\right)\right]\)

\(=\left(x+5\right)\left[x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\right]\)

\(=\left(x+5\right)\left(x+1\right)\left(x^2-x-6\right)\)

\(=\left(x+5\right)\left(x+1\right)\left(x-3\right)\left(x+2\right)\)

a ) \(==>x^3.\left(x+3\right)-\left(7x^2+27x+18\right)\)

ko xét phần x^3.( x+3 ) nữa mà mik phân tích trong ngoặc nha zo thi ko lm như vậy mà ghi lại phần đó nha

\(7x^2+21x+6x+18\)

\(7x\left(x+3\right)+6\left(x+3\right)\)

\(\left(x+3\right)\left(7x+6\right)\)

==> \(x^3.\left(x+3\right)-\left(x+3\right)\left(7x+6\right)\)

==>\(\left(x+3\right)\left(x^3-7x-6\right)\)

x - 18 - 42 = 23 - 43 - 70 - x

\(\rightarrow\) 2x = -30

\(\rightarrow\) x = -15

\(\left(-\left(x+15\right)\right)^2\) - 19 = \(3^2\) .5

\(\rightarrow\)\(x^2+30x+225\) - 19 = 45

\(\rightarrow x^2+30x+161=0\)

\(\rightarrow x^2+23x+7x+161=0\)

\(\rightarrow x\left(x+23\right)+7\left(x+23\right)=0\)

\(\rightarrow\left(x+7\right)\left(x+23\right)=0\)

\(\rightarrow\) x = -7 hoặc x = -23