# How do you factor the expression #c^4 + c^3 - 12c - 12#?

##### 1 Answer

Apr 13, 2016

#### Answer:

#### Explanation:

We can factor this quartic using grouping then the difference of cubes identity, which may be written:

#a^3-b^3 = (a-b)(a^2+ab+b^2)#

with

#c^4+c^3-12c-12#

#=(c^4+c^3)-(12c+12)#

#=c^3(c+1)-12(c+1)#

#=(c^3-12)(c+1)#

#=(c^3-(root(3)(12))^3)(c+1)#

#=(c-root(3)(12))(c^2+root(3)(12)c+root(3)(144))(c+1)#

If we allow Complex coefficients then this can be factored further as:

#=(c-root(3)(12))(c-omega root(3)(12))(c-omega^2 root(3)(12))(c+1)#

where