For what real values of x is -4 < x^4 + 4x^2 < 5 satisfied? Express your answer in interval notation.
We can narrow this expression to 0
Factor the expression into x^2(x^2+4). After setting x to 1, we can see that x must be less than 1 for the inequality to be satisfied.
Also, the expression cannot be less than 4 because x^2 cannot be negative. Setting x to 0 allows the expression to equal 4.
But x can also be between -1 and 0 because of the rule with even exponents. So the final answer is -1
Hope that helps