Question

Pls Help! 100 Points!!!
Show all work to factor x^4 − 5x^2 + 4 completely.

Answer 1

`(x+2)(x-2)(x+1)(x-1)`

Explanation:

We want to factor the expression
`x^4-5x^2+4`.

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
`u=x^2`.

Our expression is the same as:

`(x^2)^2-5(x^2)+4`

Substitute:

`u^2-5u+4`

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

`=(u-4)(u-1)`

We can now substitute back u:

`=(x^2-4)(x^2-1)`

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

`(a^2-b^2)=(a+b)(a-b)`

Therefore, we will have:

`=(x+2)(x-2)(x+1)(x-1)`

And we are done!