Question

Descompuneti in factori : x^2+3x+2 = ?
Va rog cu rezolvare . Dau 20 de puncte . va rog .

Answer 1

Metoda I: calcul direct
$x^{2} +3x+2= x^{2} +x+2x+2=x(x+1)+2(x+1)=(x+1)(x+2)$⇒
$x^{2} +3x+2=(x+1)(x+2)$
Metoda II: scriem trinomul de gradul al II-lea sub forma factorizata.
Pentru aceasta consideram ecuatia atasata:
$x^{2} +3x+2=0$
Δ=$3^{2} -4*1*2=9-8=1$⇒Δ>0⇒$x_{1,2}$∈R
$x_{1} = \frac{-3+1}{2} = \frac{-2}{2}$⇒$x_{1} =-1$
$x_{2} = \frac{-3-1}{2} = \frac{-4}{2}$⇒$x_{2} =-2$
Forma factorizata a trinomului: $ax^{2} +bx+c, a \neq 0$ este:
$ax^{2} +bx+c=a(x- x_{1})(x- x_{2})$
In cazul de fata avem ca: a=1, b=3, c=2 astfel obtinem:
$x^{2} +3x+2=1*(x-(-1))(x-(-2))=(x+1)(x+2)$⇒
$x^{2} +3x+2=(x+1)(x+2)$

Answer 2

x²+3x+2=3²+x+2x+2=x(x+1)+2(x+1)=(x+1)(x+2)