Advanced Math practice question

Answer: A. x² − 2x − 3

Divide, or match coefficients: (x − 2)(x² + bx + c) = x³ + (b − 2)x² + (c − 2b)x − 2c. So b − 2 = −4 gives b = −2, and −2c = 6 gives c = −3; check c − 2b = −3 + 4 = 1. ✓ The quotient is x² − 2x − 3.

Why the other answers are wrong

B. x² + 2x − 3

(x − 2)(x² + 2x − 3) = x³ − 7x + 6, wrong x² and x terms.

C. x² − 2x + 3

(x − 2)(x² − 2x + 3) has constant −6, not +6.

D. x² − 6x + 13

(x − 2)(x² − 6x + 13) = x³ − 8x² + 25x − 26.

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