#### If (x + 2) and (x – 3) are factors of x^{3} + ax + b, find the values of a and b. With these values of a and b, factorize the given expression.

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#### (x – 2) is a factor of the expression x^{3} + ax^{2} + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find the values of a and b. (2005)

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