Sagot :
a) Factorisation
A = 9x²+42x+49
= ((3x)² + 2 × 3x × 7 + 7²
= (3x + 7)²
B = 25 - 20x + 4x²
= 4x² - 20x + 25
= ((2x)² - 2×2x×5 + 5²
= (2x - 5)²
b) C = A - B
Réduction :
C = (3x + 7)² - (2x - 5)²
= ((3x)² + 2 × 3x × 7 + 7²) - ((2x)² - 2 × 2x × 5 + 5²)
= 9x² + 42x + 49 - (4x² - 20x + 25)
= 9x² + 42x + 49 - 4x² + 20x - 25
= 5x² + 62x + 24
Factorisation :
C = (3x + 7)² - (2x - 5)²
= [(3x+7) - (2x-5)][(3x+7) + (2x-5)]
= [3x + 7 - 2x + 5] [3x + 7 + 2x - 5]
= (x + 12)(5x+2)
Pour calculer C lorsque x = 0 tu peux utiliser la forme factorisée :
C = (x + 12)(5x + 2)
= (0 + 12) (5×0 + 2)
= 12×2
= 24
Si x = -1
C = (-1 + 12) (5×(-1) + 2)
= 11 × (-3)
= -33
Si x = -0,5
C = (-0.5 + 12) (5×(-0.5) +2 )
= 11.5 × (-2.5 + 2)
= 11.5 × (-0.5)
= - 5.75
A = 9x²+42x+49
= ((3x)² + 2 × 3x × 7 + 7²
= (3x + 7)²
B = 25 - 20x + 4x²
= 4x² - 20x + 25
= ((2x)² - 2×2x×5 + 5²
= (2x - 5)²
b) C = A - B
Réduction :
C = (3x + 7)² - (2x - 5)²
= ((3x)² + 2 × 3x × 7 + 7²) - ((2x)² - 2 × 2x × 5 + 5²)
= 9x² + 42x + 49 - (4x² - 20x + 25)
= 9x² + 42x + 49 - 4x² + 20x - 25
= 5x² + 62x + 24
Factorisation :
C = (3x + 7)² - (2x - 5)²
= [(3x+7) - (2x-5)][(3x+7) + (2x-5)]
= [3x + 7 - 2x + 5] [3x + 7 + 2x - 5]
= (x + 12)(5x+2)
Pour calculer C lorsque x = 0 tu peux utiliser la forme factorisée :
C = (x + 12)(5x + 2)
= (0 + 12) (5×0 + 2)
= 12×2
= 24
Si x = -1
C = (-1 + 12) (5×(-1) + 2)
= 11 × (-3)
= -33
Si x = -0,5
C = (-0.5 + 12) (5×(-0.5) +2 )
= 11.5 × (-2.5 + 2)
= 11.5 × (-0.5)
= - 5.75
