Complete Factorization of P(x) = x^4 + 4x^​2

[Illvoices]

how do i factor this polynomial:

P(x)=x⁴+4x^​2

 

[stapel]

how do i factor this polynomial:

P(x)=x⁴+4x^​2

This is just a simple factorization (here), much simpler than the more advanced stuff you've posted in other threads, such as this thread. Where are you getting stuck, specifically?

 

[Illvoices]

I'm supposed to find the zeros for the polynomial but i don't know where to start. I'm using a advance college base algebra book thats why i posted on intermidiate, but i guess the problem is a basic problem.

 

[ksdhart2]

Well, the problem only looks complicated and scary because you're not used to factoring quartics (4th-degree polynomials). However, notice that the given polynomial doesn't have any x³, x¹ or constant terms. That means that, behind the scenes, it's actually just an ordinary quadratic that you've solved a hundred times before. Try using the substitution u=x² and rewrite the given polynomial in terms of u. Then factor that much simpler, less daunting polynomial. Don't forget to back-substitute once you get your final u values though, because your teacher doesn't care what values of u satisfy the equation, but wants the corresponding values of x.

 

[HallsofIvy]

Surely, you can see that there is a factor of "\(\displaystyle x^2\)"?