AUT01-14

retour

\begin{align*} A(x) &= \pmb{(x-5)} (x+2) + \pmb{(x-5)}(x-7)& \\ &=(x-5)\big[(x+2)+(x-7)\big]& \\ &=(x-5)(x+2+x-7)& \\ &=(x-5)(2x-5);& \end{align*} \begin{align*} B(x) &= \pmb{x}(x+2) + 3\pmb{x}& \\ &=x\big[(x+2) + 3\big]& \\ &=x(x+2+3)& \\ &=x(x+5)\;;& \end{align*} \begin{align*} C(x) &= (x+2)\pmb{(x+1)} - 2\pmb{(x+1)}& \\ &=(x+1)\big[(x+2) - 2\big]& \\ &=(x+1)x\;;& \end{align*} \begin{align*} D(x) &= \pmb{(x+3)}^2 - (x+1)\pmb{(x+3)}& \\ &=(x+3)\big[(x+3) - (x+1)\big]& \\ &=(x+3)(x+3-x-1)& \\ &=2(x+3);& \end{align*} \begin{align*} E(x) &= 2\pmb{x(x+3)} + \pmb{x(x+3)}(x+2)& \\ &=x(x+3)\big[2 + (x+2)\big]& \\ &=x(x+3)(x+4).& \end{align*}

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code : 168