How do you factor #x^6 + 2x^5 + 3x^4 + 6x^3#?

1 Answer
George C.
Nov 15, 2015

Separate out the common factor #x^3# then factor by grouping to find:

#x^6+2x^5+3x^4+6x^3 = x^3(x^2+3)(x+2)#

Explanation:

#x^6+2x^5+3x^4+6x^3#

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

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

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

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

This has no simpler factors with Real coefficients since #x^2+3 >= 3 > 0# for all #x in RR#

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