Chapter 3 - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 293: 34

$P(x)=x^{3}(x+i\sqrt{7})(x-i\sqrt{7})$ Zeros: 0 (multiplicity 3) $\pm i\sqrt{7}$ (multiplicity 1)

Factor out $x^{3}$, $P(x)=x^{3}(x^{2}+7)$ The parentheses, $x^{2}+7=x^{2}-7(-1)=x^{2}-(i\sqrt{7})^{2}$ $=(x+i\sqrt{7})(x-i\sqrt{7})$ $P(x)=x^{3}(x+i\sqrt{7})(x-i\sqrt{7})$ Zeros: 0 (multiplicity 3) $\pm i\sqrt{7}$ (multiplicity 1)