Show all work to factor x^4 − 5x^2 + 4 completely.

Step-by-step explanation:

We want to factor the expression .

First, notice that this is in quadratic form. In other words, both the exponents have even power.

Therefore, we can make a substitution to simplify the expression.

So, let’s let .

Our expression is the same as:

Substitute:

Now, we can factor like normal. We can use -1 and -4. Therefore:

We can now substitute back u:

Both of these can be factored furthered using the difference of two squares:

Therefore, we will have:

And we are done!

c is the final answer! : )