If (x+1) is a factor of `2x^(3)+ax^(2)+2bx+1`, then find the value of a and b given that 2a-3b=4.

Explanation

To solve the problem, we need to find the values of \( a \) and \( b \) given that \( (x + 1) \) is a factor of the polynomial \( 2x^3 + ax^2 + 2bx + 1 \) and that \( 2a - 3b = 4 \).

### Step 1: Use the Factor Theorem
Since \( (x + 1) \) is a factor of the polynomial, we can use the Factor Theorem. According to the theorem, if \( (x + 1) \) is a factor, then substituting \( x = -1 \) into the polynomial should yield zero.

### Step 2: Substitute \( x = -1 \)
Substituting \( x = -1 \) into the polynomial:

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