a) [latex]w(x)=3 x^{3} + x^{2} - 2x - 3 = 3*0^{3} + 0^{2} - 2*0 - 3 = -3[/latex] [latex]w(x)=3 x^{3} + x^{2} - 2x - 3 =3*( frac{1}{2})^{3} + (frac{1}{2}) ^{2} - 2* frac{1}{2}-3 = frac{3}{8} + frac{1}{4} - 1 -3[/latex] [latex]= - 3 frac{3}{8} [/latex] [latex]w(x)=3 x^{3} + x^{2} - 2x - 3 = 3*(-2) ^{2} + (-2)^{2} - 2*(-2) - 3 =[/latex] [latex]= 12+4+4-3 = 17[/latex] [latex]w(x)=3 x^{3} + x^{2} - 2x - 3 = w(x)=3(-3) ^{3} + (-3)^{2} - 2*(-3) - 3 =[/latex] [latex]= 81 + 9 + 6 - 3 = 93[/latex] b) [latex]w(x) = -2 x^{3} + x^{2} - 5x + 2 = -2*0^{3} + 0^{2} - 5*0 + 2 = 2[/latex] [latex]w(x)=-2 x^{3} + x^{2} - 5x + 2 =-2*( frac{1}{2}) ^{3} + ( frac{1}{2}) ^{2} - 5*( frac{1}{2}) + 2 =[/latex] [latex]= - frac{1}{4} + frac{1}{4} - 2frac{1}{2} + 2 = - frac{1}{2} [/latex] [latex]w(x) = -2 x^{3} + x^{2} - 5x + 2 = -2*(-2)^{3} + (-2)^{2} - 5*(-2) + 2 =[/latex] [latex]= 16 + 4 + 10 + 2 = 32[/latex] [latex]w(x) = -2 x^{3} + x^{2} - 5x + 2 = -2*(-3)^{3} + (-3)^{2} - 5*(-3) + 2 =[/latex] [latex]= 54 + 9 + 15+2 = 80[/latex] c) [latex]w(x) = x^{3} - 4 x^{2} + 3x - 4 = 0^{3} - 4*0^{2} + 3*0 - 4 = -4[/latex] [latex]w(x) = x^{3} - 4 x^{2} + 3x - 4 = (frac{1}{2}) ^{3} - 4*( frac{1}{2}) ^{2} + 3* frac{1}{2} - 4 = [/latex][latex]= frac{1}{8} - 1 + 1 frac{1}{2} - 4 = - 3 frac{5}{8} [/latex] [latex]w(x) = x^{3} - 4 x^{2} + 3x - 4 = (-2)^{3} - 4*(-2)^{2} + 3*(-2) - 4 =[/latex][latex]= -8 - 16 -6 - 4 = -34[/latex] [latex]w(x) = x^{3} - 4 x^{2} + 3x - 4 = (-3)^{3} - 4*(-3)^{2} + 3*(-3) - 4 = [/latex][latex]= -27 - 36 - 9 - 4 = -76[/latex]
