Answer:
[tex](x+2)(x-2)(x+1)(x-1)[/tex]
Step-by-step explanation:
We want to factor the expression [tex]x^4-5x^2+4[/tex].
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 [tex]u=x^2[/tex].
Our expression is the same as:
[tex](x^2)^2-5(x^2)+4[/tex]
Substitute:
[tex]u^2-5u+4[/tex]
Now, we can factor like normal. We can use -1 and -4. Therefore:
[tex]=(u-4)(u-1)[/tex]
We can now substitute back u:
[tex]=(x^2-4)(x^2-1)[/tex]
Both of these can be factored furthered using the difference of two squares:
[tex](a^2-b^2)=(a+b)(a-b)[/tex]
Therefore, we will have:
[tex]=(x+2)(x-2)(x+1)(x-1)[/tex]
And we are done!
