Question

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

Answer 1

Answer:

The answer is $(x-1)(x+1)(x-2)(x+2)$

Step-by-step explanation:

The first step to factor this expression should be to write the $-5x^{2}$ as a difference:

$x^{4}-5x^{2}+4$

$x^{4}-x^{2}-4x^{2}+4$.

Then using factorization by agrupation you get:

$x^{2}(x^{2}-1)-4 (x^{2}-1)$

$(x^{2}-1)(x^{2}-4)$.

Then using factorization by difference of two squares, using the formula:

$(a^{2} -b^{2} )=(a-b)(a+b)$

So, we get:

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

Answer 2

Answer:

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

Step-by-step explanation:

Let u = x^2

= u^2 - 5u + 4

(Factor u^2 - 5u + 4)

= (u-1) (u-4)

Substitute back u = x^2

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

Factor x^2 - 1 and x^2 -4

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

Hope this helped... :)

If you need to see the work for yourself, copy/paste this link

https://www.symbolab.com/solver/factor-calculator/factor%20x%5E%7B4%7D%20%E2%88%92%205x%5E%7B2%7D%20%2B%204%20