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Algebra II (2018 edition)

Unit 4: Lesson 7

Polynomial identities with complex numbers
Math
Algebra II (2018 edition)
Polynomials
Polynomial identities with complex numbers
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Factor polynomials: complex numbers

CCSS.Math: HSN.CN.C.8
Google Classroom

Problem

Shayla tried to write x, start superscript, 4, end superscript, minus, 25 as a product of linear factors. This is her work:
=x4−25=(x2+5)(x2−5)Step 1=(x2+5)(x+5)(x−5)Step 2=(x+5i)(x−5i)(x+5)(x−5)Step 3\begin{aligned} &\phantom{=} x^4 - 25 \\\\ &= \blueE{(x^2+5)}\maroonE{(x^2-5)} &&\gray{\text{Step 1}} \\\\ &= \blueE{(x^2+5)}\maroonE{(x+\sqrt5)(x-\sqrt5)} &&\gray{\text{Step 2}} \\\\ &= \blueE{(x+5i)(x-5i)}\maroonE{(x+\sqrt5)(x-\sqrt5)} &&\gray{\text{Step 3}} \end{aligned}
In what step did Shayla make her first mistake?
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