Problem preview

N-CN.8 Warmup M3-045-A03-V02

Extend polynomial identities to complex numbers for higher-degree polynomial work.

Factor a cube polynomial over R and C and list roots

Problem

Factor \(x^{3}~+~1\) completely into linear factors over the complex numbers.

Answer choices

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(x+1)(x-1/2-i√3/2)(x-1/2-i√3/2)

(x+1)(x-1/2-i√3/2)(x-1/2+i√3/2)

(x+1)(x-1/2-i√3/2)(x+1/2-i√3/2)

(x-1)(x+1/2-i√3/2)(x+1/2+i√3/2)

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Curriculum context

Course: Math III
Standard: N-CN.8
Category: Number and Quantity
Domain: The Complex Number System
Objective: Extend polynomial identities to complex numbers for higher-degree polynomial work.
Problem type: Factor a cube polynomial over R and C and list roots