ANSWER
The correct answer is B
EXPLANATION
We want to factor completely,
[tex] {x}^{4} + 8 {x}^{2} - 9[/tex]
We can rewrite the above expression in the form.
[tex] {( {x}^{2}) }^{2} + 8( {x}^{2} ) - 9[/tex]
We can think of this expression as a quadratic trinomial in
[tex] {x}^{2} [/tex]
We need to split the middle term with factors of -9 that adds up to 8.
[tex] {( {x}^{2}) }^{2} - {x}^{2} + 9{x}^{2} - 9[/tex]
We factorize to obtain,
[tex] {x}^{2} ( {x}^{2} - 1) + 9( {x}^{2} - 1)[/tex]
We factor further to obtain,
[tex]({x}^{2} - 1)( {x}^{2} + 9)[/tex]
We apply difference of two squares on the leftmost factor to obtain,
[tex](x - 1)(x + 1)( {x}^{2} + 9)[/tex]
