If x + 1 is a factor of 2x³ + ax² + 2bx + 1, and 2a – 3b = 4, then the value of a + 2b is:

Correct option is C

Polynomial: 2x³ + ax² + 2bx + 1
x + 1 is a factor → f(–1) = 0
Also given: 2a – 3b = 4

Formula used:
If x + 1 is a factor, then f(–1) = 0

Solution:
f(–1) = 2(–1)³ + a(–1)² + 2b(–1) + 1 = 0
=> –2 + a – 2b + 1 = 0
=> a – 2b = 1 ...(1)

Also given:
2a – 3b = 4 ...(2)

From (1):
a = 2b + 1

Substitute into (2):
2(2b + 1) – 3b = 4
=> 4b + 2 – 3b = 4
=> b + 2 = 4
=> b = 2

Now,
a = 2(2) + 1 = 5
a + 2b = 5 + 4 = 9

Correct answer is (c)