Identify the roots of each equation. state the multiplicity of each root: 2x^5 + 12x^4 + 16x^3 - 12x^2 - 18x = 0 * include all work*

The hardest part would be how to factor it

ok, so multiplicty is how many times the root repeats
example
f(x)=(x-r1)²(x-r2) means roots are r1 multiplicty 2 and r2 multiplicty 1

if we were to factor (I think it would be done by factoring by grouping, first undsitribute the 2x)

2x(x⁴+6x³+8x²-6x-9)=0
do magic to factor this
2x(x-1)(x+1)(x+3)²=0
so in form
(x-r1) where r1 is a root
2(x-0)(x-1)(x+1)(x+3)²=0
2(x-0)(x-1)(x-(-1))(x-(-3))²=0
the roots are
-3 multiplicty 2, -1 multiplicty 1, 0 multiplicty 1, 1 multilicty 1