The provided text contains solutions to multiple-choice questions covering complex numbers, logarithms, algebraic expressions, and factoring. What were the original questions?

Step 1: Solve Question 1.
The conjugate of a complex number $a+bi$ is $a-bi$.
For the complex number $2+\sqrt{3}i$, the real part is 2 and the imaginary part is $\sqrt{3}$.
The conjugate is $2-\sqrt{3}i$.
The correct option is b.

$$\boxed{\text{b. } 2-\sqrt{3}i}$$

Step 2: Solve Question 2.
The question is $\log_? 125 = x$. Based on the options, the most likely base for 125 to result in an integer is 5. Let's assume the base is 5.

$$\log_5 125 = x$$

This means $5^x = 125$.
Since $125 = 5 \times 5 \times 5 = 5^3$, we have:

$$5^x = 5^3$$

Therefore, $x=3$.
The correct option is d.

$$\boxed{\text{d. } 3}$$

Step 3: Solve Question 3.
We need to find the value of the expression $\frac{x^2-9}{3x-2}$ at $x=3$.
Substitute $x=3$ into the expression:

$$\frac{(3)^2-9}{3(3)-2} = \frac{9-9}{9-2} = \frac{0}{7}$$ $$\frac{0}{7} = 0$$

The correct option is c.

$$\boxed{\text{c. } 0}$$

Step 4: Solve Question 4.
We need to find one of the factors of the expression $x^2-8x+12$.
To factor a quadratic expression of the form $ax^2+bx+c$, we look for two numbers that multiply to $c$ and add up to $b$.
Here, $c=12$ and $b=-8$. The two numbers are $-2$ and $-6$, because $(-2) \times (-6) = 12$ and $(-2) + (-6) = -8$.
So, the expression can be factored as:

$$x^2-8x+12 = (x-2)(x-6)$$

One of the factors is $x-2$.
The correct option is a.

$$\boxed{\text{a. } x-2}$$

Step 5: Solve Question 5.
We need to find the HCF (Highest Common Factor) of $4x^2-8x$ and $x-2$.
First, factor the expression $4x^2-8x$:

$$4x^2-8x = 4x(x-2)$$

The second expression is $x-2$.
The common factor between $4x(x-2)$ and $(x-2)$ is $x-2$.
Therefore, the HCF is $x-2$.
The correct option is c.

$$\boxed{\text{c. } x-2}$$

Step 6: Solve Question 6.
We need to solve the linear equation $\frac{12x}{7}-x=5$ for $x$.
Combine the terms with $x$:

$$\frac{12x}{7} - \frac{7x}{7} = 5$$ $$\frac{12x-7x}{7} = 5$$ $$\frac{5x}{7} = 5$$

Multiply both sides by 7:

$$5x = 5 \times 7$$ $$5x = 35$$

Divide both sides by 5:

$$x = \frac{35}{5}$$ $$x = 7$$

The correct option is d.

$$\boxed{\text{d. } 7}$$

Step 7: Solve Question 7.
We need to determine which line the point $(-2, -7)$ lies on. Substitute $x=-2$ and $y=-7$ into each equation.

*a) $y=4x+1$:

$$-7 = 4(-2)+1$$ $$-7 = -8+1$$ $$-7 = -7$$

This statement is true, so the point lies on this line.
Let's quickly check other options to confirm.

*b) $y=x+1$: $-7 = -2+1 \Rightarrow -7 = -1$ (False)

*c) $y=x+2$: $-7 = -2+2 \Rightarrow -7 = 0$ (False)

*d) $2y=3x+2$: $2(-7) = 3(-2)+2 \Rightarrow -14 = -6+2 \Rightarrow -14 = -4$ (False)
The correct option is a.

$$\boxed{\text{a. } y=4x+1}$$

Step 8: Solve Question 8.
The statement is $4+x=4 \Rightarrow x=y$. This appears to have a typo and should likely be $4+x=4 \Rightarrow x=0$ or $4+x=4+y \Rightarrow x=y$. In either case, the property used is the cancellation property with respect to addition. If $a+b=a+c$, then $b=c$.
In $4+x=4$, we can subtract 4 from both sides to get $x=0$. This is an application of the cancellation property for addition.
The correct option is b.

$$\boxed{\text{b. cancellation property w.r.t addition}}$$

Step 9: Solve Question 9.
The matrix is $\begin{bmatrix} 0 & 0 & 0 \ 0 &