How do you factor #x^4+6x^3-36x^2-216x#?

1 Answer
May 22, 2017

Answer:

#x(x-6)(x+6)^2#

Explanation:

#x^4+6x^3-36x^2-216x#

#=x(x^3+6x^2-36x-216)larr" common factor " x#

#"note that when " x=6#

#x^3+6x^2-36x-216=0#

#rArrx=6" is a root and hence " (x-6)" is a factor"#

#rArrx^2(x-6)+12x(x-6)+36(x-6)#

#=(x-6)(x^2+12x+36)#

#=(x-6)(x+6)(x+6)#

#rArrx^4+6x^3-36x^2-216x=x(x-6)(x+6)^2#