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2009-12-01T10:39:15+01:00
W(x)=3x³-3x²+4x-11
U(x)=-x³+x²-5x-3
V(x)=4x³+2x+5
rozwiazać:
W(x)+U(x) = 3x³-3x²+4x-11-x³+x²-5x-3 = 2x³ - 2x² - x - 14
W(x)-U(x) = 3x³-3x²+4x-11 - (-x³+x²-5x-3) = 3x³-3x²+4x-11+x³-x²+5x+3 = 4x³-4x²+9x-8
W(x)•U(x) = (3x³-3x²+4x-11)(-x³+x²-5x-3) = -3x⁶+3x⁵-15x⁴-9x³+3x⁵-3x⁴+15x³+9x²-4x⁴+4x³-20x²-12x+11x³-11x²+55x+33 = -3x⁶+6x⁵-22x⁴+21x³-22x²+43x+33
U(x)-[W(x)-V(x)] = -x³+x²-5x-3 - [3x³-3x²+4x-11-(4x³+2x+5)] =
-x³+x²-5x-3 - (3x³-3x²+4x-11-4x³-2x-5) = -x³+x²-5x-3 - (-x³-3x²+2x-16) = -x³+x²-5x-3+x³+3x²-2x+16 = 4x²-7x+13