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Back to Extend polynomial identities to complex numbers — Problem 3 · 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
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Warm-Up: Review What You Know

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The quadratic x2−4x+5=0x^2 - 4x + 5 = 0 has roots 2+i2 + i and 2−i2 - i (from CN.C.7).

By the root-to-factor connection: x2−4x+5=(x−r1)(x−r2)x^2 - 4x + 5 = (x - r_1)(x - r_2).

Verify: expand (x−(2+i))(x−(2−i))(x - (2+i))(x - (2-i)) and find the constant term. Enter the constant term.