Answer:
[tex]( {x}^{2} - 5)( {x}^{2} + 9) = 0[/tex]
Step-by-step explanation:
The given expresion is
[tex] {x}^{4} + 4 {x}^{2} - 45 = 0[/tex]
We can rewrite this as:
[tex] ({ {x}^{2}) }^{2} + 4 {x}^{2} - 45 = 0[/tex]
We obtained a quadratic equation in x²
Let us split the middle term to get:
[tex]({ {x}^{2}) }^{2} + 9 {x}^{2} - 5{x}^{2} - 45 = 0[/tex]
We factor by grouping to get:
[tex] {x}^{2} ( {x}^{2} + 9) - 5( {x}^{2} + 9) = 0[/tex]
We factor further to get:
[tex]( {x}^{2} - 5)( {x}^{2} + 9) = 0[/tex]
The correct answer is A.
