Question

Cum descompun aceasta expresie: y^4+2y^3-28y^2-8y+96=0
y^=la puterea
Sa fie explicita descompunerea

Answer 1

Notam expresia cu f(y) si separam termani sub forma: 
$f(y)=y^4+6y^3-4y^3-24y^2-4y^2-24y+16y+96=y^3(y+6)-$$-4y^2(y+6)-4y(y+6)+16(y+6)=(y+6)(y^3-4y^2-4y+16)=$$(y+6)[y^2(y-4)-4(y-4)]=(y+6)(y-4)(y^2-4)=$(y+6)(y-4)(y+2)(y-2). Daca se cer radacinile ecuetiei f(y)=0, egalam fiecare paranteza cu 0 si se obtine: $y_{1}=-6, y_{2}=4, y_{3}=-2, y_{4}=2.$