# How do you factor the expression #x^4+4x^3+6x^2+4x+1#?

##### 1 Answer

Feb 3, 2016

#### Explanation:

The coefficients of this quartic are

These are the coefficients of the binomial expansion of

In our example,

Alternatively, first notice that if we give the coefficients alternating signs then they sum to

#1-4+6-4+1 = 0#

Hence

#x^4+4x^3+6x^2+4x+1 = (x+1)(x^3+3x^2+3x+1)#

If we give the coefficients of the remaining cubic factor alternating signs then again they add to

#1-3+3-1 = 0#

Hence

#x^3+3x^2+3x+1 = (x+1)(x^2+2x+1)#

Similarly we find