Question

descompuneti in factori polinomul : Xla puterea a 2 -5X-14, si :3Xla puterea a 2 -4 X-4

Answer 1

Eu,stiu(din,cate,imi,mai,amintesc...)ca,se,face,cu,artificii,de,calcul
x²-5x-14=x²-4x+4-x-18=(x-2)²-(x-2)-20

3x²-4x-4=4x²-4x+1-x²-5=(2x-1)²-(x²+5)

De,aici,incolo,nu,mai,stiu...Poate,preia,cineva,ceva,din,ce-am,facut...

Answer 2

x^2-5x-14=0
∆=b^2-4ac
∆=(-5)^2-4•1•(-14)
∆=25+56
∆=81
√∆=√81=9
x1=(-b-√∆)/2a
x1=(5-9)/2•1=-4/2=-2
x2=(-b+√∆)/2a
x2=(5+9)/2•1=14/2=7
Descompunerea se poate face dupa formula:
a(x-x1)(x-x2)=
=1(x-(-2))•(x-7)
=(x+2)(x-7)

3x^2-4x-4=0
∆=b^2-4ac
∆=(-4)^2-4•3•(-4)
∆=16+48
∆=64
√∆=√64=8
x1=-b-√∆/2a
x1=(4-8)/2•3=-4/6=-2/3
x2=-b+√∆/2a
x2=4+8/2•3=12/6=2
a(x-x1)(x-x2)=
=3(x+2/3)(x-2)
=(3x+2)(x-2)