Oblicz wartości wielomianu w dla: x=0, x=1/2, x=-2, x=-3
a)
w(x)= 3x^{3} + x^{2} - 2x - 3
w(0)=0+0-0-3=-3
w(\frac{1}{2})=3*(\frac{1}{2})^3+(\frac{1}{2})^2-2*\frac{1}{2}-3=3*\frac{1}{8}+\frac{1}{4}-1-3=\frac{3}{8}+\frac{2}{8}-4=\frac{5}{8}-4=-(4-\frac{5}{8})=-3\frac{3}{8}
w(-2)=3*(-2)^3+(-2)^2-2*(-2)-3=-24+4+4-3=-19
w(-3)=3*(-3)^3+(-3)^2-2*(-3)-3=-81+9+6-3=-69
b)
w(x)= -2x^{3} + x^{2} -5x+2
w(0)=0+0-0+2=2
w(\frac{1}{2})=-2*(\frac{1}{2})^3+(\frac{1}{2})^2-5*\frac{1}{2}+2=-\not2^1*\frac{1}{\not8^4}+\frac{1}{4}-\frac{5}{2}+2=-\frac{1}{4}+\frac{1}{4}-2,5+2=-0,5
w(-2)=-2*(-2)^3+(-2)^2-5*(-2)+2=16+4+10+2=32
w(-3)=-2*(-3)^3+(-3)^2-5*(-3)+2=54+9+15+2=80
c)
w(x)= x^{3}-4x^{2}+3x-4
w(0)=0-0+0-4=-4
w(\frac{1}{2})=(\frac{1}{2})^3-4*(\frac{1}{2})^2+3*\frac{1}{2}-4=\frac{1}{8}-4*\frac{1}{4}+\frac{3}{2}-4=\frac{1}{8}-1+\frac{12}{8}-4=\frac{5}{8}-4=-(4-\frac{5}{8})=-3\frac{3}{8}
w(-2)=(-2)^3-4*(-2)^2+3*(-2)-4=-8-16-6-4=-34
w(-3)=(-3)^3-4*(-3)^2+3*(-3)-4=-27-36-9-4=-76
d)
w(x)= -x^{4} +5x^{3}-4x-10
w(0)=0+0-0-10=-10
w(\frac{1}{2})=-(\frac{1}{2})^4+5*(\frac{1}{2})^3-4*\frac{1}{2}-10=-\frac{1}{16}+5*\frac{1}{8}-2-10=-\frac{1}{16}+\frac{5}{8}-12=
=-\frac{1}{16}+\frac{10}{16}-12=\frac{9}{16}-12=-(12-\frac{9}{16})=-11\frac{7}{16}
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w(-2)=-(-2)^4+5*(-2)^3-4*(-2)-10=-16-40+8-10=-58
w(-3)=-(-3)^4+5*(-3)^3-4*(-3)-10=-81-5*27+12-10=-214