Question

Descompuneti in factori trinomul de gradul doi : P(x) =3x la a doua - 2x -1

Answer 1

P(x)=$3 x^{2} -2x-1=3 x^{2} -3x+x-1=3x(x-1)+(x-1)=(x-1)$(3x+1)

Answer 2

Pentru a descompune trinomul rezolvam ecuatia de gradul ll si aflam radacinile x1 si x2

ax²+bx+c=a(x-x1)(x-x2)

3x²-2x-1=0
a=3
b=-2
c=-1
∆=b²-4ac=(-2)²-4*3*(-1)=4+12=16

x1=(-b+√∆)/2a=(-(-2)+√16)/2*3=(2+4)/6=6/6=1

x2=(-b-√∆)/2a=(-(-2)-√16)/2*3=(2-4)/6=-2/6=-⅓

x1=1 si x2=-⅓

3x²-2x-1=3[x-(-⅓)](x-1)=(3x+1)(x-1)