Which expression is equivalent to x4 + 4x² - 45?

Step-by-step explanation:

x4 + 4x² - 45 = x^4 + 4x^2 - 45. Use " ^ " to indicate exponentiation.

Temporarily substitute p for x^2. Then we have:

p^2 + 4p - 45, or

(p + 9) (p - 5)

But p = x^2.

Therefore, our expression becomes

(x^2 + 9) (x^2 - 5)

We could stop here or we could factor further.

Hint: x^2 - 5 = (x - √5) (x + √5); (x^2 + 9) factors into imaginary roots.