## College Algebra 7th Edition

$P(x)=(x-2)(x+2)(x^2+1)$ Zeros: $-2$ and $2$. Refer to the graph below.
Factor the polynomial completely to obtain: \begin{align*} P(x)&=(x^2-4)(x^2+1)\\ &=(x-2)(x+2)(x^2+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-2&=0 &\text{or}& &x+2=0& &\text{or}& &x^2+1=0\\ x&=2 &\text{or}& &x=-2& &\text{or}& &\text{(no real solution)} \\ \end{align*} The zeros of the function are $-2$ and $2$. Use a graphing utility to graph P(x). Refer to the graph above.