Question

Factor the expression completely over the complex numbers. y^3+2y^2+16y+32

Answer 1

Answer:

  (y +2)(y +4i)(y -4i)

Step-by-step explanation:

This lends itself to factoring by grouping. Then the quadratic factor can be considered to be the difference of squares and factored accordingly.

  (y^3 +2y^2) +(16y +32) = y^2(y +2) +16(y +2) = (y^2 +16)(y +2)

  = (y +2)(y^2 -(√-16)^2) = (y +2)(y^2 -(4i)^2)

  = (y +2)(y -4i)(y +4i)