How do you factor #x^4 + 8x^3 - 2x^2 - 16x#?

1 Answer
Apr 9, 2016

Answer:

#x^4+8x^3-2x^2-16x=x(x-sqrt(2))(x+sqrt(2))(x+8)#

Explanation:

First note that all of the terms are divisible by #x#, so separate that out as a factor first, then factor by grouping...

#x^4+8x^3-2x^2-16x#

#=x(x^3+8x^2-2x-16)#

#=x((x^3+8x^2)-(2x+16))#

#=x(x^2(x+8)-2(x+8))#

#=x(x^2-2)(x+8)#

#=x(x-sqrt(2))(x+sqrt(2))(x+8)#