Question
Sat June 30, 2012 By:

Can you please help me to solve this problem?

Expert Reply
Sat June 30, 2012
Let f(x) = 2x3 + ax2 + bx - 2.
(x + 2) is a factor of f(x), so f(-2) = 0. 
f(-2) = 2(-2)3 + a(-2)2 + b(-2) - 2 = -16 + 4a - 2b - 2 = 0, 
ie,    4a - 2b = 18                                       ... (1)
Division by (2x - 3) leaves a remainder of 7, so f(3/2) = 7 
f(3/2) = 2(3/2)3 + a(3/2)2 + b(3/2) + 2 = 7
Simplifying this you will get another equation in terms of a and b.
 
Solve the two equations to get the values of a and b as 3 and -3 respectively.
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