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Course: Precalculus?>?Unit 3

Lesson 4: Identities with complex numbers

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Factor polynomials: complex numbers

Google Classroom

Shayla tried to write

x^{4} ? 25

as a product of linear factors. This is her work:

\begin{aligned} x^{4} ? 25 \\ = (x^{2} + 5) (x^{2} ? 5) & Step 1 \\ = (x^{2} + 5) (x + \sqrt{5}) (x ? \sqrt{5}) & Step 2 \\ = (x + 5 i) (x ? 5 i) (x + \sqrt{5}) (x ? \sqrt{5}) & Step 3 \end{aligned}

In what step did Shayla make her first mistake?

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