A) Step 1: Factorize the quadratic expression for the area.

a) Step 1: Factorize the quadratic expression for the area.
The area of the rectangular garden is given by $A = x^2 - 4x - 21$.
To factorize this quadratic, we need to find two numbers that multiply to $-21$ and add up to $-4$.
These numbers are 3 and $-7$.
So, the expression can be factored as:

$$A = (x + 3)(x - 7)$$

Step 2: Determine the dimensions of the garden.
For a rectangle, Area = Length $\times$ Width.
Therefore, the dimensions of the garden are the factors we found.
Length $= (x + 3)$ units
Width $= (x - 7)$ units
Since dimensions must be positive, $x-7 > 0$, which means $x > 7$.

The dimensions of the garden are $\boxed{(x+3) \text{ and } (x-7)}$.

b) Step 1: Calculate the perimeter of the garden.
The perimeter $P$ of a rectangle with length $L$ and width $W$ is given by $P = 2(L + W)$.
Using the dimensions from part a):

$$P = 2((x + 3) + (x - 7))$$ $$P = 2(x + 3 + x - 7)$$ $$P = 2(2x - 4)$$ $$P = (4x - 8) \text{ meters}$$

Step 2: Calculate the cost of fencing.
The cost of fencing wire is Ksh 1.50 per meter.
Total cost = Perimeter $\times$ Cost per meter
Total cost = (4x - 8) \times 1.50$$ Total cost = 1.5(4x - 8) Total cost $= (6x - 12) \text{ Ksh}

The cost of fencing the garden is $\boxed{(6x - 12) \text{ Ksh}}$.