\(\displaystyle{x}^{{{3}}}-{6}{x}^{{{2}}}+{11}{x}-{y}={6}\)

\(\displaystyle{y}={x}^{{{3}}}-{6}{x}^{{{2}}}+{11}{x}-{6}\)

\(\displaystyle{P}{\left({x}\right)}={x}^{{{3}}}-{6}{x}^{{{2}}}+{11}{x}-{6}\)

\(\displaystyle{P}{\left({z}\right)}={1}-{6}+{11}-{6}={0}\)

(x-l) is a talov of p(x)

Diviwng p(x) by (x-l) we get

\(\displaystyle{2}{\left({x}\right)}={x}^{{{2}}}-{3}{x}-{2}{x}+{6}\)

\(\displaystyle{2}{\left({x}\right)}={x}{\left({x}-{3}\right)}-{2}{\left({x}-{3}\right)}\)

\(\displaystyle{2}{\left({x}\right)}={\left({x}-{2}\right)}{\left({x}-{3}\right)}\)

\(\displaystyle{p}{\left({x}\right)}={\left({x}-{1}\right)}{2}{\left({x}\right)}\)

\(\displaystyle{p}{\left({x}\right)}={\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{3}\right)}\)

Zowes of polynaval are x=1,2,3

\(\displaystyle{y}={x}^{{{3}}}-{6}{x}^{{{2}}}+{11}{x}-{6}\)

\(\displaystyle{P}{\left({x}\right)}={x}^{{{3}}}-{6}{x}^{{{2}}}+{11}{x}-{6}\)

\(\displaystyle{P}{\left({z}\right)}={1}-{6}+{11}-{6}={0}\)

(x-l) is a talov of p(x)

Diviwng p(x) by (x-l) we get

\(\displaystyle{2}{\left({x}\right)}={x}^{{{2}}}-{3}{x}-{2}{x}+{6}\)

\(\displaystyle{2}{\left({x}\right)}={x}{\left({x}-{3}\right)}-{2}{\left({x}-{3}\right)}\)

\(\displaystyle{2}{\left({x}\right)}={\left({x}-{2}\right)}{\left({x}-{3}\right)}\)

\(\displaystyle{p}{\left({x}\right)}={\left({x}-{1}\right)}{2}{\left({x}\right)}\)

\(\displaystyle{p}{\left({x}\right)}={\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{3}\right)}\)

Zowes of polynaval are x=1,2,3