Could someone please help me with these two math questions?

Question

Factor the following expressions completely over the complex numbers.

1. x² + 18

2. y⁴ + 12y² + 36

Answer 1

 First find the roots.  

 

1. If x² + 18 = 0, then x² = -18

 

    So, x = ±√-18 = ±√18 i = ±3√2 i

 

    x² + 18 = (x - 3√2 i)(x + 3√2 i)

 

2. y⁴ + 12y² + 36 = 0

 

   (y² + 6)(y² + 6) = 0

 

    y = ±√6 i (each root has multiplicity 2)

 

    y⁴ + 12y² + 36 =  (y - √6 i)²(y + √6 i)²