Problem preview

N-CN.8 Warmup M2-058-A06-V02

Extend polynomial identities to complex numbers, such as factoring sums of squares over the complex numbers.

Solve \(u^2+b^2=0\) by factoring into complex conjugates

Problem

Factor \((x-2)^{2}+16\) as a conjugate product over \(ℂ\), set each factor equal to zero, and isolate \(x\) in \(\text{both}~\text{equations}\).

Answer choices

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Rewrite 16 as 4² and factor (x-2)²+16 as (x-2+4i)²=0, so the only solution is x=2-4i.

Rewrite 16 as 4² and factor (x-2)²+16 as (x-2+4i)(x-2-4i)=0, so the solutions are x=2+4i and x=2-4i.

Rewrite 16 as 4² and factor (x-2)²+16 as (x-2+4)(x-2-4)=0, so the solutions are x=6 and x=-2.

Rewrite 16 as 4² and factor (x-2)²+16 as (x-2+16i)(x-2-16i)=0, so the solutions are x=2+16i and x=2-16i.

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Curriculum context

Course: Math II
Standard: N-CN.8
Category: Number and Quantity
Domain: The Complex Number System
Objective: Extend polynomial identities to complex numbers, such as factoring sums of squares over the complex numbers.
Problem type: Solve \(u^2+b^2=0\) by factoring into complex conjugates