Calculați: 

2x – 7x – x + 9x =

7x – 12x – 5x + 14x =

6x – 21x + 4x – 11x =

4x2 + 5x – 8 + x2 – 1 – 7x =

3x2 – 5 – 6x – x2 + 7 – 3x =

3x2 – 5x – 7x – 9x2 + 16x =

6x3 – x2 + 3x – 9 – 2x + 8x2 =

4x3 – 2x2 – 6x2 – 8x3 + 9x2 =

163x2 – 114x – 137x2 + 96x =

272x3 – 149x2 – 183x + 167x2 – 195x3 + 241x =

201x3 – 125x + 171x2 + 237x – 156x3 – 243x2 =

43x – 32 + 15x2 – 37 + 14x – 52x2 + 79 – 37x – 16x2 =

27x3 – 43 + 22x – 63x2 + 47 – 54x + 32x2 – 65x + 91 =

[image]

[image]

13,4x2 – 5,24 + 3,61x + 4,15 – 6,71x2 + 4,9x =

0,3x – 7,1x2 + 2,37 + 5,62x2 – 3,4x – 6,2 =

3,(1)x2 – 5,2x + 4,3(2) + 6,(3)x – 5,6x2 + 7,1 =

1,(2)x – 6,4x2 – 3,2(5)x + 8,(2)x2 – 3,(4) + 5,6 =

[image][image]



Calculati:

(– 72x5 + 48x4 – 36x3 + 24x2):(– 12x2) =

(– 56x7 – 42x6 + 28x5 – 70x3):(14x3) =

[– 5x·(8x4 – 4x3) – 10x·(6x2 – 4x)]:(– 20x2) =

[– 12x2·(6x3-4x2) + 9x·(4x2 – 8x)]:(– 12x2) =

[x2 – 3x2·(x – 3) + (4x2 – 3x)·(3x2 – 2x)] : (– 4x2) =

[2x·(x3 – 3x2 + 4x – 6) – 4·(x2 – 3x)] : (2x2) =

[4x2·(3x2 – 5x + 6) – (x2 – 6x)·(x3 – 4x)] : (– x3) =

[6x·(x4 – 2x3 + 3x2 + x – 1) – 3x·(– 4x3 + 2x – 2)] : (6x3) =

[(3x2 – 2x + 1)·(2x + 3) – 3·(– 3x2 + 1)] : (2x) =

[(3x2 – 2x – 4)·(x – 2) – (x2 + 4x – 8)·(x + 1)] : (8x) =

[(x2 – x + 2)·(4x – 3) – (2x2 + x + 1)·(x – 6)] : 8x) =

[(6x2 – 4x)·(2x3 – 3x2) – (x2 – x)·(x2 + 2) – x·(x2 – 2x + 2)] : (– 3x3) =

[(3x – 2)·(2x + 4) – (2x2 + 4x + 6)·(x – 1) + 2·(x3 + 1)] : (– 2x) =

[(4x + 1)·(3x + 2) – (x2 – 3x + 1)·(x + 2) + x2·(x – 1)] : (– 4x) =

[(4x + 3)·(x – 1) – 2·(3x + 2)·(x – 3) – 3·(x + 3)] : (– 2x) =

[(x ++2)·(x2 + 2x – 2) – 4x·(x – 1) + 4·(x3 + x + 1)] : (– 5x) =

(6a2x3y2 – 12a4x2y3 – 9a3x3y3) : (– 3a2x2y2) =

(3a4x2 – 5a3x3 + 6a2x4) : (2a4x4) =

(– 5x3y2 – 6x2y2 – x4y4) : (– x3y3) =

(4a3b3 – 6a2b2 + 2a2b) : (2a2b) =

(4x3 + 6x2 – x) : [image]

(– 2x4 – 3x3 + x2) : [image]

(x4 + 4x3 – 6x2 – 8x) : (– 0,2x) =

(16x3 – 5x2 + 3x) : (0,5x) =

(3x – 2)·(x + 3) =

(5x – 2)·(2x + 3) =

[image]

[image]

(x3 – 3x2 + 2x – 4)·(2x2 – x + 3) =

[5x – 2 – (3x + 1)]·[2x + 5 – (4x – 3)] =

[(3x – 1)·(x + 2) – 3x·(x + 2)]·(4x – 3) =

(5x – 1)·[12x·(x + 1) – (6x + 5)·(2x – 1)] – 4x·(10x + 3) =

(2x3 – x2 + 3x – 5)·(x2 – 2x – 3) =

[3x – 2 – (4x – 3)]·[2x + 1 – (3x + 2)] =

[(6x – 1)·(x + 2) – 3x·(2x + 3)]·(x – 2) =

[8x·(x – 3) – (2x – 1)·(4x + 3)]·(x + 1) + 13x·(2x + 1) =

3x·(2x2 – 5x – 3) – 6·(x3 – 2x2 – x + 3) + 3·(x2 + x + 6) =

(x3 – 2x2 – 3x + 4)·(x2 + 2x + 5) =

[image]

(x – 2)·(3x + 1)·(2x – 3) – 6·(x3 – 2x + 1) =

[(4x – 3)·(3x + 2) – 2x·(6x – 1)]·(2x + 1) – 2·(x2 – 3) =

Descompuneţi în factori:

49 – 4x2 =

36x2 – 25 =

64 – x2 =

25x2 – 4 =

4x2 – 9 =

x2 – 2x – 8 =

x2 + x – 6 =

x2 – x – 2 =

x2 – 2x – 3 =

9x2 – 6x + 1 =

25x2 – 20x + 4 =

4x2 – 4x + 1 =

4x2 + 4x + 1 =

4x2 – 12x + 9 =

9x4 – 12x3 – 18x2 =

6x4 – 12x3 + 24x2 =

4x3 – 12x2 + 16x =

12x4 – 18x3 + 30x2 =

x4 – 25x2 + 60x – 36 =

x4 – 16x2 + 24x – 9 =

x4 – 25x2 + 60x – 36 =

2x·(x + 2) – 3·(x + 2) =

6x·(5x + 1) – 7·(5x + 1) =

7x·(2x – 1) – 5·(2x – 1) =

(5x + 2)2 – (x – 3)2 =

(3x – 1)2 – (2x + 3)2 =

(2x + 3)2 – (x – 2)2 =

x4 – 6x3 + 13x2 – 12x + 4 =

x4 – 2x3 – 3x2 + 4x + 4 =

x4 – 4x2 – 12x – 9 =



Calculaţi: 

(5x + 2)2 =

(x – 4)2 =

(3x – 2)2 =

(2x – 3)2 =

(4x – 3)2 =

(4x – 1)2 =

(2x2 – x – 1)2 =

(x2 – 3x + 2)2 =

(x2 – 2x – 1)2 =

(3x2 – x + 2)2 =

(x2 – x + 3)2 =

(2x2 – 3x + 1)2 =

(2x + 7)·(2x – 7) =

(3x – 5)·(3x + 5) =

(2x – 3)·(2x + 3) =

(x – 7)·(x + 7) =

(x – 4)·(x + 4) =

(3x – 2)·(3x + 2) =

(4x – 1)·(2x – 3) =

(3x – 2)·(x + 3) =

(5x + 2)·(2x – 3) =

(2x + 3)·(x – 2) =

(5x – 2)·(x + 3) =

(x – 2)·(3x + 1) =

7x2 – 5 + 3x – x2 + 4x–6x =

6x2 + 3 – 2x – 5x2 – 1 + 4x =

8x2 – 4 + 5x – x2 + 6 – 4x =

3x2 – 5 + 8x – 4x2+7–3x =

2x2 + 5 – 4x – 3x2 – 4 + 6x =

5x2 – 3 – 3x – 2x2 + 5 + 4x =

5·(2x–1)·(x+2)–x·(10x–3) =

2·(3x+2)·(x–1) – 6x·(x–3) =

4·(3x–2)·(x+1)–6x·(2x–1) =

3·(2x–1)·(x+2)–x·(6x–1) =

4·(2x–3)·(x+1)–8x·(x–2) =

6·(2x–1)·(x+2)–3x·(4x–1) =



Calculaţi: 

[image]



Fie: A = 1x3 – 8x2 + x – 3, B = 2x2 – x + 1, C = 2x – 3

Calculaţi:

  1. A – B – C =

  2. A – 2·B – 3·C =

  3. A – (x – 1)·B – x2·C =

  4. A·C – B·C =

  5. A – B2 – C2 – (2x + 3)·C =



Fie: A = 2x3 – x2 + 6x – 1, B = x2 – 2x + 2, C = x – 2

Calculaţi:

  1. A + B – C =

  2. A – 2·B + 3·C =

  3. A – (x – 1)·B – x2·C =

  4. A·C – B·C =

  5. A – B2 – C2 – (x + 2)·C =



Fie: A = 3x3 – x2 + 2x – 1, B = 4x2 – 2x – 2, C = 2x + 1

Calculaţi:

  1. A – B +C =

  2. A + 2·B – 3·C =

  3. A – (x – 1)·B – x2·C =

  4. A·C – B·C =

  5. A – B2 – C2 – (2x – 1)·C=



Să se arate că:

  1. 4x2 + y2 - 4x + 6y + 12 ≥ 0 unde x∈R

  2. 2x2 + y2 - 2√2x -2y +9 ≥ 0 unde x∈R



Să se arate că:

[image]

[image]

[image]



Să se determine minimul expresiei:

  1. 25x2 + 30x +13 unde x∈R

  2. x2 -14x + 50 unde x∈R



Să se determine maximul expresiei:

  1. –x2 - 2x + 2 unde x∈R

  2. –x2 – 10x – 15 unde x∈R



Să se determine x şi y ştiind că:

  1. x2 + y2 – 10x + 4y +29 = 0

  2. 4x2 + 3y2 +4x - 6√3y +10 = 0



Să se arate că:

  1. 4n+2n+1+1 este un patrat perfect.

  2. 42n+22n+1+1 este un patrat perfect.

  3. 9n+2×3n+1 este un patrat perfect.