How do you factor #h(x)= x^4 + 4x^3 + x^2 - 6x#?

1 Answer
Jul 22, 2015

Answer:

#h(x) = x(x-1)(x+2)(x+3)#

Explanation:

Extract the common factor of #x# from the terms of #x^4+4x^3+x^2-6x#
#color(white)("XXXX")##=x(x^3+4x^2+x-6)#

Considering the term: #x^3+4x+x-6#
Notice that the coefficients of the first 3 terms sum to the negative of the final constant
#rarr (x-1)# is a factor of this expression.

Using synthetic division (or whatever method you choose):
#color(white)("XXXX")##= x(x-1)(x^2+5x+6)#

We can use standard AC methods to factor this final term:
#color(white)("XXXX")##= x(x-1)(x+2)(x+3)#