How do you factor: #y= x^3 - 4x^2 + 4x - 16 #?

1 Answer
Mar 12, 2016

Answer:

Factor by grouping to find:

#y = x^3-4x^2+4x-16#

#=(x^2+4)(x-4)#

#=(x-2i)(x+2i)(x-4)#

Explanation:

Factor by grouping:

#y = x^3-4x^2+4x-16#

#=(x^3-4x^2)+(4x-16)#

#=x^2(x-4)+4(x-4)#

#=(x^2+4)(x-4)#

That's as far as you can go with Real coefficients: #(x^2+4)# has no linear factors with Real coefficients since #x^2+4 >= 4 > 0# for all #x in RR#.

If you allow Complex coefficients then we can go a little further:

#=(x^2-(2i)^2)(x-4)#

#=(x-2i)(x+2i)(x-4)#