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Answer:
2x² − 4x + 3
Step-by-step explanation:
x = 2/3 is a root of both the numerator and the denominator, so it divides evenly. Therefore, one method is to factor by grouping:
6x³ − 16x² + 17x − 6
6x³ − 4x² − 12x² + 17x − 6
2x² (3x − 2) − (12x² − 17x + 6)
2x² (3x − 2) − (4x − 3) (3x − 2)
Divided by 3x − 2:
2x² − (4x − 3)
2x² − 4x + 3
Another method is to use long division (see image).
