The polynomial $f (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + b$ when divided by $(x - 1)$ and $(x + 2)$ leaves the remainder $5$ and $19$ respectively. Find the values of 'a' and 'b'. Hence find the remainder when $f (x)$ is divided by $(x - 2)$ .

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Scarlett Discussed

The polynomial

f (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + b

when divided by

(x - 1)

and

(x + 2)

leaves the remainder

5

and

19

respectively. Find the values of 'a' and 'b'. Hence find the remainder when

f (x)

is divided by

(x - 2)

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