Check whether x3-x+1 is a multiple of 2-3x

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Solution

Dear student
$L e t p (x) = x^{3} - x + 1 a n d q (x) = 2 - 3 x \Rightarrow q (x) = 0 \Rightarrow 2 - 3 x = 0 \Rightarrow x = \frac{2}{3} I f t h e g i v e n p o l y n o m i a l m u s t b e t h e m u l t i p l e o f 2 - 3 x t h e n p (\frac{2}{3}) = 0 \Rightarrow {(\frac{2}{3})}^{3} - \frac{2}{3} + 1 \Rightarrow \frac{8}{27} - \frac{2}{3} + 1 \Rightarrow \frac{8 - 18 + 27}{27} \Rightarrow \frac{17}{27} \neq 0 S o, t h e g i v e n p o l y n o m i a l i s n o t a m u l t i p l e o f 2 - 3 x$
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