Statement: x - 1 is a factor of 4x^2 - 9x - 6.

To determine whether x - 1 is a factor of the given quadratic expression, we need to check if the expression is divisible by x - 1. If it is, then x - 1 is a factor; otherwise, it is not a factor.

Division Method:

Step 1: Write the given expression in the form of (x - 1) * quotient + remainder.
4x^2 - 9x - 6 = (x - 1) * (4x + a) + b

Step 2: Equate the coefficients of like terms on both sides of the equation.
For the x^2 term: 4x^2 = x * (4x + a)
This gives us a = 0.

For the x term: -9x = -1 * (4x + a) + b
Simplifying, we get -9x = -4x - b - a
Since a = 0, the equation becomes -9x = -4x - b.
This gives us b = -5x.

For the constant term: -6 = -1 * b
Substituting the value of b, we get -6 = 5x.

Step 3: Solve the equation obtained in the previous step.
-6 = 5x
Dividing both sides by 5, we get x = -6/5.

Conclusion:

Since the remainder is not zero when dividing the given quadratic expression by x - 1, x - 1 is not a factor of 4x^2 - 9x - 6. Therefore, the correct answer is option 'B' (False).