Question

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

Answer 1

`(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)`