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?
- A. 2x² + x − 1Correct
- B. 2x² − x − 1
- C. 2x² + x + 1
- 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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