[tex]5a)\\\\w(x)=(1-2x)(1+x)(3x^2+2)=(1+x-2x-2x^2) (3x^2+2)=(1-x-2x^2) (3x^2+2)=\\\\=3x^2-3x^3-6x^4+2-2x-4 x^2=-6x^4-3x^3-x^2-2x+2\\\\ Stopien\ wielomianu\ - \ to\ najwyzsza\ potega\ x-a\ w\ tym\ wielomianie,\\\\czyli\ mamy\ 4\ stopien\ wielomianu\\\\wyraz\ wolny ,\ to\ liczba:\ 2[/tex]
[tex]b)\\\\w(x)=( 2x^3+\frac{1}{2}x+1)(x^2-x-\frac{1}{4})=\\\\=2x^5-2x^4-\frac{1}{2}x^3+\frac{1}{2} x^3-\frac{1}{2}x^2-\frac{1}{8}x+x^2-x-\frac{1}{4}=\\\\=2x^5-2x^4 + \frac{1}{2}x^2-1\frac{1}{8}x -\frac{1}{4} \\\\ mamy\ 54\ stopien\ wielomianu\\\\wyraz\ wolny ,\ to\ liczba:\ (-\frac{1}{4})[/tex]
[tex]6)\\\\u (x)= x^3+3x-1 ,\ \ \ w(x)= x^4-6x^3-2x^2\\\\f(x)=u(x)*w(x) = (x^3+3x-1)*(x^4-6x^3-2x^2)=\\\\=x^7-6x^6-2x^5+ 3x^5 -18x^4-6x^3-x^4+6x^3+2x^2=\\\\=x^7-6x^6+ x^5 -19x^4+2x^2[/tex]
[tex]6)\\\\ g(x)=[ u(x) ]^2-w(x)= (x^3+3x-1)^2-(x^4-6x^3-2x^2)=\\\\=x^6 +6x^4 -2x^3+9x^2+6x+1-x^4+6x^3+2x^2=\\\\=x^6+5x^4+4x^3 +11x^2 +6x+1 \\\\\\ (a+b+c)^2 =a^2+2ab+2ac+b^2+2bc+c^2[/tex]
