Question

wiedząc ze W(x)=4xdo potegi3-5xdo pot.2+3x-2, P(x)=-xdo pot.2 +7x+2, Q(x)=7-4xdo pot 2-6x wykonaj wskazane działania W(x)-P(x) W(x)+2Q(x) P(x)razyQ(x) 7W(x)-5P(x)-P(x)razy Q(x) 1/2[W(x)razy Q(x)-P(x)] upotrzadkuj malejaco otrzymany wielomian

Answer 1

W(x)=4x³-5x²+3x-2  

P(x)=-x² +7x+2  

Q(x)=-4x²-6x +7

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W(x)-P(x)=

=4x³-5x²+3x-2-(-x²+7x+2)=

=4x³-5x²+3x-2+x²-7x-2=

=4x³-4x²-4x-4

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W(x)+2Q(x)=

=4x³-5x²+3x-2+2*(-4x²-6x +7)=

=4x³-5x²+3x-2-8x²-12x +14=

=4x³-13x²-9x+12

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P(x)Q(x)=

=(-x² +7x+2)*(-4x²-6x +7)=

=4x⁴-22x³-57x²+37x+14

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7W(x)-5P(x)-P(x)Q(x)=

=7(4x³-5x²+3x-2)-5*(-x² +7x+2)-(-x² +7x+2)*(-4x²-6x +7)=

=28x³-35x²+21x-14+5x²-35x-10-4x⁴+22x³+57x²-37x-14=

=-4x⁴+50x³+27x²-51x-38

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1/2[W(x)Q(x)-P(x)]=

=1/2[(4x³-5x²+3x-2)*(-4x²-6x +7)-(-x² +7x+2)]=

=1/2[-16x⁵-24x⁴+46x³-45x²+33x-14+x²-7x-2]=

=1/2[-16x⁵-24x⁴+46x³-44x²+26x-16]=

=-8x⁵-12x⁴+23x³-22x²+13x-8