Answer:
He made the following mistake, he assumed that polynomial [tex](x^{2}+1) = (x^{2}-1)[/tex], having for granted that [tex]x^{2}+1[/tex] has two real roots, instead of two complex roots.
Step-by-step explanation:
He made the following mistake, he assumed that polynomial [tex](x^{2}+1) = (x^{2}-1)[/tex], having for granted that [tex]x^{2}+1[/tex] has two real roots, instead of two complex roots. The true factorized form of the fourth grade polynomial is:
[tex]r(x) = (x^{2}+1)\cdot (x^{2}-9)[/tex]
[tex]r(x) = (x- i)\cdot (x+i)\cdot (x+3)\cdot (x-3)[/tex]
