How do you factor #32x^5 + 64x^4 + 16x#?

1 Answer
Mar 30, 2018

Answer:

#(x+(2+sqrt(2))/2)(x-(sqrt(2)-2)/2)#

Explanation:

1) Factor
You can factor 16 out of all three terms
#16(2x^5+4x^4+x)#
You can also factor #x# from all three terms
#16x(2x^4+4x^3+1)#

2) You plug it into the quadratic formula.
#x=(-b+-sqrt(b^2-4ac))/(2a)#
You get the roots of
#x=-(2+sqrt(2))/2, (sqrt(2)-2)/2#

3) You make them factored
#(x+(2+sqrt(2))/2)(x-(sqrt(2)-2)/2)#