Find the remainder if $x - 1$ is divided by $5 x^{3} - 2 x^{2} + 3 x - 22$

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Solution

By remainder theorem when $f (x)$ is divided by $x - a$ , remainder is $f (a)$
So When $5 x^{3} - 2 x^{2} + 3 x - 22$ is divided by $x - 1$ ,
Remainder is $5 (1)^{3} - 2 (1)^{2} + 3 (1) - 22$ = $- 16$

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