Question

2x pătrat+x-3=
4x pătrat-4x-35=
n=x(x-3)(x pătrat-3x+4)+4, p.p oricare ar fi x €R

Answer 1

n= (x²-3x) ( x²-3x +4) +4
notam x²-3x    cu  a
⇒a (a+4) + 4 = a² +4a +4 = (a+2)²

inlocuim pe a cu x²-3x
n= (a+2)²= (x²-3x + 2 )²  care este p.p.

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2x² +x -3 = 2x² +x -2 -1 =2(x²-1) + x-1 = 2(x+1)(x-1) + x-1= (x-1)(2x+2 +1)= (x-1)(2x+3)

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4x² -4x -35 = 4x² -25 -4x -10 = (2x-5)(2x+5) -2(2x+5) = (2x+5) (2x-5 -2) = (2x+5)(2x -7)