Question

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

Answer 1

Answer:

$(x+2)(x-2)(x+1)(x-1)$

Step-by-step 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!