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Back to Extend polynomial identities to complex numbers — Problem 4 · Task Set 14

Exercises: Extend Polynomial Identities to Complex Numbers

Factor completely over the complex numbers. Verify by expanding when asked.

Grade 9·20 problems·~40 min·Common Core Math - HS Number and Quantity·standard·hsn-cn-c-8
Work through problems with immediate feedback
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Fluency Practice

1.

The quadratic x2+2x+5=0x^2 + 2x + 5 = 0 has roots −1+2i-1 + 2i and −1−2i-1 - 2i.

Write the factored form: $x^2 + 2x + 5 = (x - $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   $)(x - $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   )$.

Enter the two roots (the numbers being subtracted), separated.

first root (with sign):
second root (with sign):