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a fost răspuns

Descompuneti: dau 50 de puncte
1) x²-4=
2) x²-4x+4=
3)4x²+4x+1=
4)x²-4x+3=
5)4x²-4x=
6)x³+2x²+x=
7) (x-3)³- x+3=
8) x³-x²-x+1=
9)x⁴-1=
10) x⁴+1=
Dau coroana. Clasa 7


Răspuns :

1) = (x-2)(x+2)
2) =( x-2)²
3) = 4x² +4x + 2 -1 = 4x² -1 + 4x + 2 = (2x+1)(2x-1) + 2 (2x+1) = (2x+1)(2x-1+2)=
=(2x+1)(2x+1) = (2x+1)²
4) = x²-3x -x +3 = x(x-1) -3(x-1) = (x-1)(x-3)
5)=4x (x-1)
6) =x(x²+2x+1) = x(x+1)²
7) = (x-3)³ - (x-3) = (x-3) par.patrata (x-3)²-1 inchidem paranteza patrata
= (x-3) ( x-3-1)(x-3+1)= (x-3)(x-4)(x-2)
8) = x³-x-x²+1 = x³ - x - (x-1) = x(x²-1) - (x-1) = x(x-1)(x+1) - (x-1) = (x-1)(x+1)(x-1)
   = (x-1)² (x+1)
9) = (x²+1) (x²-1) = (x²+1)(x+1)(x-1)
10) = x la a patra -2x² +1 +2x² = (x²+1)² -2x² = (x² +1 +x√2)(x² +1 - x√2)