Please show me how to divide (3x^3 + 2x^2  6x + 4) by (x + 2) 
First of all, you might like to remind yourself how long division works with numbers.
Click to see a worked example.
The system is similar for algebraic division.
Write the problem as shown on the right. Note that the terms are written in descending powers of x. 

Always focus first on the leading terms. Find how many times x goes into 3x^{3}. The result is 3x^{2}. 

Now multiply the whole of x + 2 by 3x^{2}. The result is 3x^{3} + 6x^{2}. 

Subtract, giving a remainder of 4x^{2}. Bring down the 6x. 

Now focus again on the leading terms. Find how many times x goes into 4x^{2}. The result is 4x. Write this on the solution line. 

Multiply the whole of x + 2 by 4x. 

Subtract, giving a remainder of 2x. Bring down the 4. 

Find how many times x goes into 2x. The result is 2. Write this on the solution line. 

Multiply the whole of x + 2 by 2. The result is 2x + 4. 

Subtract. This means that x + 2 is a factor of the original cubic. 
So, the result of the division 