Question

6x^3-16x^2+17x-6?/3x-2

Answer 1

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).