For this case we have the following polynomial:
\(x ^ 4 + 8x ^ 2 - 9
\)
We make the following change of variables:
\(u = x ^ 2
\)
Rewriting we have
\(u ^ 2 + 8u - 9
\)
Factoring the second order polynomial we have:
\((u + 9) (u-1)
\)
Then, returning the change we have:
\((x ^ 2 + 9) (x ^ 2-1)
\)
Finally, we factor the expression in the parentheses of the second term:
\((x ^ 2 + 9) (x + 1) (x-1)
\)
Answer:
the completely factored form is:
\((x ^ 2 + 9) (x + 1) (x-1)\)
