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Vexalord
@Vexalord
April 2019
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Je n'arrive pas à résoudre cet exercice, pouvez-vous m'aider ?
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Bonjour
9x^4+12x^2+4=(3x²+2)²
2)9x^4-15x^3+12x²-10x+4
=(3x²+2)²-15x^3-10x
=(3x²+2)²-5x(3x²+2)
=(3x²-2)[3x²+2-5x]
3x²-5x+2=(3x²-3x)-(2x-2)
=3x(x-1)-2(x-1)
=(x-1)(3x-2)
donc
(3x²-2)(3x²-5x+2)=(3x²-2)(x-1)(3x-2)
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9x^4+12x^2+4=(3x²+2)²
2)9x^4-15x^3+12x²-10x+4
=(3x²+2)²-15x^3-10x
=(3x²+2)²-5x(3x²+2)
=(3x²-2)[3x²+2-5x]
3x²-5x+2=(3x²-3x)-(2x-2)
=3x(x-1)-2(x-1)
=(x-1)(3x-2)
donc
(3x²-2)(3x²-5x+2)=(3x²-2)(x-1)(3x-2)