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Factoriser autant que possible les expressions suivantes :

• $I(x)=5x^2 + 7x$;   Corrigé
  \[\begin{aligned} I(x)&=5x^2 + 7x& \\ &= x(5x + 7)& \end{aligned}\]
• $J(x)=x^2 + x$;   Corrigé
  \[\begin{aligned} J(x)&=x^2 + x& \\ &= x(x+1)& \end{aligned}\]
• $K(x)=3x^3 - 6x^2 + 9x$;   Corrigé
  \[\begin{aligned} K(x)&=3x^3 - 6x^2 + 9x& \\ &= 3x(x^2-2x+3)& \end{aligned}\]
• $L(x)= x^2 - 4$;   Corrigé
  \[\begin{aligned} L(x)&=x^2 - 4& \\ &= x^2 - 2^2& \\ &= (x-2)(x+2)& \end{aligned}\]
• $M(x)=9x^2 - 25$;   Corrigé
  \[\begin{aligned} M(x)&=9x^2 - 25& \\ &= (3x)^2 - 5^2& \\ &= (3x-5)(3x+5)& \end{aligned}\]
• $N(x)=x^2 + 6x + 9$.   Corrigé
  \[\begin{aligned} N(x)&=x^2 + 6x + 9& \\ &= x^2 + 2\cdot 3\cdot x + 3^2& \\ &= (x+3)^2& \end{aligned}\]

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