Answer:
[tex]=(x^2-3)(x^2-2)[/tex]
Step-by-step explanation:
So we have the expression:
[tex]x^4-5x^2+6[/tex]
And we wish to factor it.
First, let's make a substitution. Let's let u be equal to x². Therefore, our expression is now:
[tex]=u^2-5u+6[/tex]
This is a technique called quadratic u-substitution. Now, we can factor in this form.
We can use the numbers -3 and -2. So:
[tex]=u^2-2u-3u+6[/tex]
For the first two terms, factor out a u.
For the last two terms, factor out a -3. So:
[tex]=u(u-2)-3(u-2)[/tex]
Grouping:
[tex]=(u-3)(u-2)[/tex]
Now, substitute back the x² for u:
[tex]=(x^2-3)(x^2-2)[/tex]
And this is the simplest form.
And we're done!
