Question

Which expression is equivalent to x^4 + 4x^2 - 45?

Answer 1

`( {x}^(2) - 5)( {x}^(2) + 9) = 0`

Explanation:

The given expresion is

`{x}^(4) + 4 {x}^(2) - 45 = 0`

We can rewrite this as:

`({ {x}^(2)) }^(2) + 4 {x}^(2) - 45 = 0`

We obtained a quadratic equation in x²

Let us split the middle term to get:

`({ {x}^(2)) }^(2) + 9 {x}^(2) - 5{x}^(2) - 45 = 0`

We factor by grouping to get:

`{x}^(2) ( {x}^(2) + 9) - 5( {x}^(2) + 9) = 0`

We factor further to get:

`( {x}^(2) - 5)( {x}^(2) + 9) = 0`

The correct answer is A.