SUP03-08

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1.a. $3x - 6 = 3x - 3\cdot 2 = 3(x-2)$.

1.b. Donc \[\begin{aligned} A(x) &= 3x + 6 + (x+2)(x-8)& \\ &=3\underline{(x+2)} + \underline{(x+2)}(x-8)& \\ &=(x+2)\big[3 + (x-8)\big]& \\ &=(x+2)(3+x-8)& \\ &=(x+2)(x-5).& \end{aligned}\]

2. \[\begin{aligned} B(x) &= x^2 - 4 + (x-1)(x+2)& \\ &=(x-2)\underline{(x+2)} + (x-1)\underline{(x+2)}& \\ &=(x+2)\big[(x-2) + (x-1)\big]& \\ &=(x+2)(x-2+x-1)& \\ &=(x+2)(2x-3).& \end{aligned}\] \[\begin{aligned} C(x) &= \underline x^2 + 4\underline x + (x-1)(x+4)& \\ &=x\underline{(x+4)} + (x-1)\underline{(x+4)}& \\ &=(x+4)\big[x + (x+1)\big]& \\ &=(x+4)(x+x+1)& \\ &=(x+4)(2x+1).& \end{aligned}\]

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code : 186