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EXERCICE 4
Factoriser en utilisant une identité remarquable.
1. A = 25+ 70x +49x²
2. B = 1-16x²
3. C = 4x² - 12x +9
4. D = 49x² + 112x+64
5. E= 9x² - 42x +49
6. F = 16-9x²
7. G = 25x² 30x+9
8. H = 1+ 16x+64x²
9. I = 4x² - 36

Sagot :

HIRONDELLE52

Bonsoir,

1. A = 25+ 70x +49x²

= (5+7x) ²

2. B = 1-16x²

= (1-4x) (1+4x)

3. C = 4x² - 12x +9

= (2x -3)²

4. D = 49x² + 112x+64

= (7x +8)²

5. E= 9x² - 42x +49

= (3x - 7)²

6. F = 16-9x²

= (4-3x) ( 4+3x)

7. G = 25x² + 30x+9

= (5x +3)²

ou

(5x-3)²

si 25x² - 30x+9

8. H = 1+ 16x+64x²

= (1+8x)²

9. I = 4x² - 36

= (2x-6) (2x+6)

MOZI

Bonjour,

1. A = 25 + 70x + 49x² = 5² = 2 × 5 × 7x + (7x)² = (5 + 7x)²

2. B = 1 - 16x² = 1² - (4x)² = (1 - 4x) (1 + 4x)

3. C = 4x² - 12x +9 = (2x)² - 2 × 2x × 3 + 3² = (2x - 3)²

4. D = 49x² + 112x + 64 = (7x)² + 2 × 7x × 8 + 8² = (7x + 8)²

5. E= 9x² - 42x + 49 = (3x)² - 2 × 3x × 7 + 7² = (3x - 7)²

6. F = 16 - 9x² = 4² - (3x)² = (4 - 3x) (4 + 3x)

7. G = 25x² + 30x + 9 = (5x)² + 2 × 5x × 3 + 3² = (5x + 3)²

8. H = 1 + 16x + 64x² = 1² + 2 × 1 × 8x + (8x)² = (1 + 8x)²

9. I = 4x² - 36 = (2x)² - 6² = (2x - 6) (2x + 6)

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