S=6x^3-3x^2+4x-2
T=x^3-x^2-2x-2
a)
W=S-3T
W=6x^3-3x^2+4x-2-3(x^3-x^2-2x-2)=
=6x^3-3x^2+4x-2-(3x^3-3x^2-6x-6)=
=6x^3-3x^2+4x-2-3x^3+3x^2+6x+6=
=3x^3+10x+4
b)
W=\frac{1}{3} S + \frac{2}{3} T
W=\frac{1}{3}(6x^3-3x^2+4x-2)+\frac{2}{3}(x^3-x^2-2x-2)=
=2x^3-x^2+\frac{4}{3}x-\frac{2}{3}+\frac{2}{3}x^3-\frac{2}{3}x^2-\frac{4}{3}x-\frac{4}{3}=
=2\frac{2}{3}x^3-1\frac{2}{3}x^2-\frac{6}{3}=
=2\frac{2}{3}x^3-1\frac{2}{3}x^2-2