Given, f(x) = 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8 and x – 2 is a factor of f(x).
We know that when a polynomial f (x) is divided by (x – a), the remaining is f from the remainder theorem (a).
So, x – 2 = 0; x = 2
Hence, f(2) = 0
2(2)5 – 6(2)4 – 2a(2)3 + 6a(2)2 + 4a(2) + 8 = 0
64 – 96 – 16a + 24a + 8a + 8 = 0
-24 + 16a = 0
16a = 24
Thus, value of a = 1.5