16Hit1600
Advanced MathVery hardQuadratic factor of a cubic

Advanced Math practice question

The polynomial 2x³ − 5x² − 4x + 3 has (x − 3) as a factor. Which of the following is the other factor?

  1. A. 2x² + x − 1Correct
  2. B. 2x² − x − 1
  3. C. 2x² + x + 1
  4. D. 2x² − 11x − 1

Answer: A. 2x² + x − 1

Dividing by (x − 3), or checking that (x − 3)(2x² + x − 1) expands to the polynomial.

Why the other answers are wrong

B. 2x² − x − 1
(x − 3)(2x² − x − 1) has middle terms −7x², not −5x².
C. 2x² + x + 1
The constant would be −3, not +3.
D. 2x² − 11x − 1
The x² coefficient would be −17.

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