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