What is the value of a when g(x) = x^3+ax+b is divided by (x-1)(x-2)?

a = - 8 and b = 9

Explanation:

Using the Remainder Theorem.

p(x) divided by (x - a) has remainder p(a)

p(1) = 1³ + a + b = 2⇒ 1 + a +b = 2 ⇒ a + b = 1 (1)

p(2)=2³ + 2a + b = 1 ⇒ 8 +2a + b =1 ⇒ 2a + b = - 7 (2)

(2) - (1) gives a = - 8

substitute a = - 8 into (1) : - 8 + b = 1 ⇒ b=9

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