$\text { If } x = \sqrt { 3 } \text { is a root of } x ^ { 3 } - x ^ { 2 } - 3 x + 3 = 0$

question 113

Multiple Choice

$\text { If } x = \sqrt { 3 } \text { is a root of } x ^ { 3 } - x ^ { 2 } - 3 x + 3 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

• A) \(( x + 1 ) ( x + \sqrt { 3 } ) ^ { 2 } ; - 1 , \sqrt { 3 }\)
• B) \(( x + 1 ) ^ { 2 } ( x - \sqrt { 3 } ) ; - 1 , \sqrt { 3 }\)
• C) \(( x + 1 ) ( x + \sqrt { 3 } ) ^ { 2 } ; 1 , - \sqrt { 3 }\)
• D) \(( x + 1 ) ( x - \sqrt { 3 } ) ^ { 2 } ; - 1 , \sqrt { 3 }\)
• E) \(( x - 1 ) ( x - \sqrt { 3 } ) ( x + \sqrt { 3 } ) ; 1 , \sqrt { 3 } , - \sqrt { 3 }\)

---

Definitions:

Foramen Ovale

An opening in the septum between the two atria of the heart in a fetus, which normally closes soon after birth.

Fetal Circulation

The circulatory system in a fetus that includes special structures like the umbilical cord, ductus arteriosus, and foramen ovale, facilitating the exchange of oxygen and nutrients between the fetus and mother.

Arterial Duct

A blood vessel in fetuses that connects the pulmonary artery to the descending aorta, allowing blood to bypass the lungs.

Umbilical Cord

Cord connecting the fetus to the placenta, through which blood vessels pass.