Honors Algebra 2: Extra Practice on Factoring over the Complex Numbers

• Class: Honors Algebra 2
• Author: Peter Atlas
• Algebra and Trigonometry: Structure and Method, Brown

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Solve by factoring over the complex nubers:

1. \( \displaystyle x^3 + x = 0 \)
Solution

\( \displaystyle x = \left\{ 0, \pm i \right\} \)

2. \( \displaystyle x^3 - 3x^2 + 4x - 12 = 0 \)
Solution

\( \displaystyle x = \left\{3, \pm 2i \right\} \)

3. \( \displaystyle x^4 - 81 \)
Solution

\( \displaystyle \left\{ \pm 3, \pm 3i \right\} \)

4. \( \displaystyle x^4 + 17x^2 + 16 \)
Solution

\( \displaystyle \left\{ \pm 4i, \pm i \right\} \)

5. \( \displaystyle x^4 - 29x^2 + 100 = 0 \)
Solution

\( \displaystyle \left\{ \pm 2, \pm 5 \right\} \)