Răspuns:
Explicație pas cu pas:
1c) f+g=X²-9X³+X⁴+8+X-X²-X⁴=8+X-9X³.
g+h=8+X-X²-X⁴+4X-X³+6X⁴=8+5X-X²-X³+5X⁴
f+g+h=8+X-9X³+4X-X³+6X⁴=8+5X-10X³+6X⁴.
2. Opusul polinomului f este -f.
a) -f=-(-2+5X-(3/5)X²+X³)=2-5X+(3/5)X²-X³.
b) -f = -11+X²+X³-4X⁵.
c) -f = -11+X²+X³-4X⁵.
d) - f = -9+3X²-13X³+√5X⁴
3.
a) (-5+7X²-13X³)+(-3+4X-X³+5X⁴)-(8-3X-4X²+X⁵)= -5+7X²-13X³-3+4X-X³+5X⁴-8+3X+4X²-X⁵=-16+7X+11X²-14X³+5X⁴-X⁵.
b) (2X-X²+4X³)-(-5+11X-6X²)+(X²-3X⁴)-(4X-X²+6X⁵)= 2X-X²+4X³+5-11X+6X²+X²-3X⁴-4X+X²-6X⁵=5-13X+7X²+4X³-3X⁴-6X⁵.
c) (-6+2X-X²)-(4X-X²+X³)+(7+X²-5X⁴)=-6+2X-X²-4X+X²-X³+7+X²-5X⁴=
1-2X+X²-X³-5X⁴.
