## College Algebra 7th Edition

$P(x)=-x(2x-1)(x+1)$ Zeros: $-1, 0, \text{ and } \dfrac{1}{2}$ Refer to the graph below.
Factor the polynomial completely to obtain: \begin{align*} P(x)&=-x(2x^2+x-1)\\ &=-x(2x-1)(x+1) \end{align*} To find the zeros, use the Zero-Product Property by equating each factor to $0$, then solve each equation to obtain: \begin{align*} -x&=0 &\text{or}& &2x-1=0& &\text{or}& &x+1=0\\ x&=0 &\text{or}& &2x=1& &\text{or}& &x=-1\\ x&=0 &\text{or}& &x=\frac{1}{2}& &\text{or}& &x=-1\\ \end{align*} Use a graphing utility to graph $P(x)$. Refer to the graph above.