Question

1) Descompuneti in factori:
a) x²-y²-4yz-4z²

b) x²-25+2x³+x²

c) (x²+y²-2²)²-4x²y²

d) 25a²-4b²+12bc-9c²

2) Aratati ca (2x+3)³-4(2x+3) este divizibil cu 3 oricare ar fi X∈Z

3) Descompuneti in factori:

(x²+2x-8) (x²-4x+4)


AJUTOORRR VA ROOG FRUMOOOS AM NEVOIE URGEEENT!!!!!! DAU COROANA SI PUNCTE IN PLUS!!!!

Answer 1

a) x²-y²-4yz-4z²=x²-(y²+4yz+4z²)=x²-(y+2z)²=(x-y-2z)(x+y+2z)

b) x²-25+2x³+x²=aici cred ca e ceva scris gresit

c) (x²+y²-2²)²-4x²y² =(x²+y²-2²-2xy)(x²+y²-2²+2xy) =[(x-y)²-2²][(x+y)²-2²)] =
=(x-y-2)(x-y+2)(x+y-2)(x+y+2)

d) 25a²-4b²+12bc-9c²=25a²-(4b²-12bc+9c²)=
=(5a)²-(2b-3c)²=(5a-2b+3c)(5a+2b-3c)

2) Aratati ca (2x+3)³-4(2x+3) este divizibil cu 3 oricare ar fi X∈Z
(2x+3)³-4(2x+3)=(2x+3)[(2x+3)²-4]=(2x+3)(2x+3-2)(2x+3+2)=
=(2x+3)(2x+1)(2x+5)
 

3)(x²+2x-8) (x²-4x+4)=(x²-2x+4x-8)(x-2)²=[x(x-2)+4(x-2)](x-2)²=(x-2)(x+4)(x-2)²=
=(x+4)(x-2)³