Question

Folosind metoda gruparii,descompuneti in factori polinomul:
a)X³+X²+X+1
b)2X³-3X²+2X-3
c)X²Y-Y²Z+X²Z-YZ²
d)2X³+XY²-2X²Y-Y³

Answer 1

a) x²(x+1) + 1(x+1) = (x+1) (x²+1)
b) x²(2x-3) +1 (2x-3)= (2x-3) (x²+1)
c) y(x²-yz) + z(x²-yz) = (x²-yz) (y+z)
d) x(2x²+y²) -y(2x²+y²) = (2x²+y²) (x-y)

Answer 2

a) X³+X²+X+1=(X³+X²)+X+1=X²(X+1)+(X+1)=(X²+1)(X+1)
b) 2X³-3X²+2X-3=(2X³+2X)-(3X²+3)=2X(X²+1)-3(X²+1)=(2X-3)(X²+1)
c) X²Y-Y²Z+X²Z-YZ²=(X²Y+X²Z)-(Y²Z+YZ²)=X²(Y+Z)-YZ(Y+Z)=(X²-YZ)(Y+Z)
d) 2X³+XY²-2X²Y-Y³=(2X³-2X²Y)+(XY²-Y³)=2X²(X-Y)+Y²(X-Y)=(2X²+Y²)(X-Y)