Question

Check whether (2 - 3x is a factor of (x^3 - x + 1)​

Answer 1

2 - 3x = 0

3x = 2

x = ⅔

then ,

x³ - x + 1 = 0 (if it is a factor)

= (⅔)³ - (⅔) + 1

= 8/27 - 2/3 + 1

$= \frac{8}{27} - \frac{2}{3} + 1 = \frac{8}{27} - \frac{18}{27} + \frac{27}{27} = \frac{27 + 8 - 18}{27} \\ \\ \\ \huge= \frac{35}{27}$

hence , 2-3x is not a factor