Question

Buna ziua v-as ruga daca se poate sa rezolvati o problema, a cateva supuncte. Va multumesc!

1) Descompuneti in factori;

a) x³+2x²-16(x+2)
b) 36(x-2)²-25(x+1)²
c)16(x+5)²-9(2x-3)²
d)25x²-4(x²+2x-3)²
e)(x+√3)²-(2√3)²
f)(y-√2)²-(2√2)²
g)(√3x-1)²-3
h)(2x+√5)²-45
i)(x²+6x+9)-(y²-4y+4)
j)(x²-2x+1)-4y²
k)36x²+12x+1-49y²

Answer 1

a) ...= x^2(x+2)-16(x+2)=(x+2)(x-4)(x+4) ;
b) ...=[6*(x-2)]^2 - [5*(x+1)]^2=[6(x-2)+5(x+1)][6(x-2)-5(x+1)]=
       =(6x-12+5x+5)(6x-12-5x-1)=(11x-7)(x-13) ;
c) ...=[4(x+5)+3(2x-3][4(x+5)-3(2x-3)]=(4x+20+6x-9)(4x+20-6x+9)=(10x+11)(-2x+29);
d) ...=[5x+2(x^2+2x-3)][5x-2(x^2+2x-3)]=(5x+2x^2+2x-6)(5x-2x^2+4x+6)=
       =(2x^2+7x-6)(-2x^2+9x+6) = ...
e) ...=[x+rad3+2rad3)(x+rad3-2rad3)=(x+3rad3)(x+rad3) ;

restul poate mai tarziu !