If $x = - 1$ Is a Root Of $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$

question 60

Multiple Choice

If $x = - 1$ is a root of $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

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

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Definitions:

Mid-ocean Ridge

An underwater mountain range, formed by plate tectonics, that encircles the globe and is the site of new oceanic crust formation.

Terranes

Geologically distinct regions that may have been brought together by past tectonic processes.

Linear Island Chain

A series of islands aligned in a straight or nearly straight line, often created by volcanic activity along a tectonic plate boundary or hotspot.

Hot Spots

Regions in the Earth's mantle that are exceptionally hot, causing volcanic activity at the Earth's surface, independent of tectonic plate boundaries.