Question

Descompuneti in factori :
a)(x+2)la a doua -x-2
b)(t+8 )la a doua -t-8
c)(x+1)la a doua +3x+3
d)2x la a treia (x la a treia +1)-x la a treia (x la a treia +1)+x la a treia +1
e)(x la a doua +x+1)la a doua -x la a doua -x-1
Va rog sa ma ajutati cat mai repede.Multumesc..

Answer 1

[tex](x+2)^2-x-2=x^2+4+4x-x-2=x^2-3x+2 \\ x^2-3x+2= \\ x^2-x-2x+2=x(x-1)-2(x-1)=(x-1)(x-2) \\ \\ (x+8)^2-x-8=x^2+64+16x-x-8=x^2+15x+56 \\ x^2+15x-56= \\ x^2+7x+8x-56=x(x+7)+8(x+7)=(x+7)(x+8) \\ \\ (x+1)^2+3x+3=x^2+1+2x+3x+3=x^2+5x+4 \\ x^2+5x+4= \\ x^2+x+4x+4=x(x+1)+4(x+1)=(x+1)(x+4) \\ \\ 2x^3(x^3+1)-x^3(x^3+1)+x^3+1= \\ 2x^6+2x^3-x^6-x^3+x^3+1=x^6+2x^3+1 \\ x^6+2x^3+1=(x^3)^2+2*x^3*1+1^2=(x^3+1)^2 \\ \\ [/tex]