If (x – 2) is a factor of 2x3 – 7x2 + 11x + 5a, find the value of a.
It is given in the question that (x – 2) is a factor of 2x3 – 7x2 + 11x + 5a
Let f (x) = 2x3 – 7x2 + 11x + 5a
Now, x – 2 = 0
x = 2
∴ f (2) = 0
2 (2)3 – 7 (2)2 + 11 (2) + 5a = 0
16 – 28 + 22 + 5a = 0
38 – 28 + 5a = 0
10 + 5a = 0
5a = - 10
a = 
a = - 2
Hence, the value of a = - 2
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