Question

VA ROG, DAU COROANA !!!
Descompunerii în produs de factori ireductibili expresia
$( {x}^{2} + 2x)( {x}^{2} + 2x - 2) - 3$
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Answer 1

Răspuns:

(x+1)²(x+3)(x-1)

Explicație pas cu pas:

fie x²+2x=t

atunci

t(t-2)-3=0

t²-2t-1-2

t²-1-2(t+1)

(t-1)(t+1) -2(t+1)

(t+1) (t-1-2)

(t+1) (t-3)

(x²+2x+1)(x²+2x-3)

(x+1)²(x²+3x-x-3)

(x+1)²(x(x+3)-(x+3))

(x+1)²(x+3)(x-1)

Answer 2

vom nota x²+2x cu y

y(y-2)-3=y²-2y-3=y²-3y+y-3=y(y-3)+(y-3)=(y-3)(y+1)=(x²+2x-3)(x²+2x+1)=(x²+3x-x-3)(x+1)²=[x(x+3)-(x+3)](x+1)²=(x-1)(x+3)(x+1)²

Kawaiimath