Question

Factor completely, or state that the polynomial is prime.y^6 - 256y^2

Answer 1

We can see that our polynomial is equal to

`y^6-256y^2=y^2(y^4-256)`

Now, we can factorize the term in parenthesis as

`y^4-256=(y^2+16)(y^2-16)`

Similarly,

`y^2-16=(y+4)(y-4)`

finally, we obtain

`y^6-256y^2=y^2(y^2+16)(y+4)(y-4)`