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

Question

asked Dec 26, 2021 220k views

1 Answer

Chandra Eskay · Answer 1 · 2021-12-31T02:28:08+0000

Answer:

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

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.