Răspuns:
Explicație pas cu pas:
1) a) f = 2-5x+4x³ ; g = 3x+2x²-x³-4x⁴ ; h = 6-x+x³-4x⁴
f+g = 2-5x+4x³+3x+2x²-x³-4x⁴ = 2-2x+2x²+3x³-4x⁴
g+h = 3x+2x²-x³-4x⁴+6-x+x³-4x⁴ = 6+2x+2x²-8x⁴
f+g+h = 2-5x+4x³+3x+2x²-x³-4x⁴+ 6-x+x³-4x⁴= 8-3x+2x²+4x³-8x⁴
b) f = 10-4x+x² ; g = -5+x²-3x³+x⁴ ; h = -8+2x-5x²+7x³
f+g = 10-4x+x²-5+x²-3x³+x⁴= 5-4x+2x²-3x³+x⁴
g+h = -5+x²-3x³+x⁴-8+2x-5x²+7x³= -13+2x-4x²+4x³+x⁴
f+g+h = 10-4x+x²-5+x²-3x³+x⁴ -8+2x-5x²+7x³=-3-2x-3x²+4x³+x⁴
c) f = x²-9x³+x⁴ ; g = 8+x-x²-x⁴ ; h = 4x-x³+6x⁴
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 = x²-9x³+x⁴+ 8+x-x²-x⁴ +4x-x³+6x⁴=8+5x-10x³+6x⁴
2) a) f = -2+5x-3/5 x²+x³ => opusul lui f = -f = 2-5x+3/5 x²-x³
b) f = 11-x²-x³+4x⁵ => -f = -11+x²+x³-4x⁵
c) f = 9-3x²+13x³-√5x⁴ => -f = -9+3x²-13x³+√5x⁴
3) a) (-5+7x²-13x³)+(-3+4x-x³+5x⁴)-(8-3x-4x²+x⁵) =
= -5-3-8+4x+3x+7x²-4x²-13x³-x³+5x⁴-x⁵ = -16+7x+3x²-14x³+5x⁴-x⁵
b) (2x-x²+4x³)-(-5+11x-6x²)+(x²-3x⁴)-(4x-x²+6x⁵) =
= 5+2x-11x-4x-x²+6x²+x²+x²+4x³-3x⁴-6x⁵ = 5-13x+7x²+4x³-3x⁴-6x⁵
c) (-6+2x-x²)-(4x-x²+x³)+(7+x²-5x⁴) =
= -6+7+2x-4x-x²+x²+x²-x³-5x⁴ = 1-2x+x²-x³-5x⁴
