## Algebra 2 Common Core

-1, 0, and $\frac{1}{2}$
First, factor the polynomial completely: $\\y=x(2x^2+x-1) \\y=x(2x-1)(x+1).$ Equate each unique factor to zero, then solve each equation: $x=0 \text{ or } 2x-1=0 \text{ or } x+1=0 \\x=0 \text{ or } x = \frac{1}{2} \text{ or } x=-1.$ Thus, the zeros are 0, -1, and $\frac{1}{2}$, each with multiplicity one.