Question

Keller performed the work below to express the polynomial in factored form:

Answer 1

Answer:

He made the following mistake, he assumed that polynomial $(x^{2}+1) = (x^{2}-1)$, having for granted that $x^{2}+1$ has two real roots, instead of two complex roots.

Step-by-step explanation:

He made the following mistake, he assumed that polynomial $(x^{2}+1) = (x^{2}-1)$, having for granted that $x^{2}+1$ has two real roots, instead of two complex roots. The true factorized form of the fourth grade polynomial is:

$r(x) = (x^{2}+1)\cdot (x^{2}-9)$

$r(x) = (x- i)\cdot (x+i)\cdot (x+3)\cdot (x-3)$