When f(x)= 3ax^3 + 2ax^2 - 7x + 3 is divided by 2x+1 the remainder is -a/2 . Determine the value or values of a.

Answer 1

By the Remainder theorem
f(-1/2) = -a/2
3a(-1/8) + 2a(1/4) - 7(-1/2) + 3 = -a/2
multiply by -1/8
3a - 4a + 28 + 24 + 8a = 0
7a = -52
a = -52/7

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