Question

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

Answer 1

Answer:

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

Step-by-step 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.