using factor theorem, find the value of 'a', if 2x4-ax3+4x2-x+2 is divisible by 2x+1

By remainder theorem we have,
2x + 1 = 0
2x = -1
x = -1/2

p(x) = 2x4 - ax3 + 4x2 - x + 2
p(-1/2) = 2 * (-1/2)4 - a * (-1/2)3 + 4 * (-1/2)2 - (-1/2) + 2
            = 2 * 1/16 + a/8 + 1 + 1/2 + 2
            = 1/8 + a/8 + 1/2 + 3
            = a/8 + (1 + 4 + 24)/8
            = a/8 + 29/8

By factor theorem we have,
     p(x) = 0
=> a/8 + 29/8 = 0
=> a/8 = -29/8
=> a = (-29 * 8)/8
=> a = -29

Hence, by factor theorem value 'a' is -29.
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