**Solving Long Division Method - Polynomial Division**

Polynomial division is a method used to divide two polynomials. It is an important concept in algebra and is often used to solve problems related to polynomials. The long division method is one of the most common ways to perform polynomial division. In this method, we divide the polynomial into smaller parts and simplify the division step by step until we obtain the quotient and remainder.

**Step 1: Arrange the polynomials**

Before starting the long division method, we need to arrange the polynomials in descending order of their degrees. For example, let's consider the division of polynomial P(x) by polynomial Q(x). Arrange P(x) and Q(x) such that the degree of P(x) is greater than or equal to the degree of Q(x).

**Step 2: Divide the first term**

To start the long division, we divide the first term of the dividend (P(x)) by the first term of the divisor (Q(x)). Write the quotient obtained above the line.

**Step 3: Multiply and subtract**

Multiply the entire divisor (Q(x)) by the quotient obtained in step 2. Write the result below the dividend (P(x)) and subtract it from the dividend. This step helps to eliminate the highest degree term from the dividend.

**Step 4: Bring down the next term**

After subtracting, bring down the next term from the dividend and write it next to the result obtained in step 3. This becomes the new dividend.

**Step 5: Repeat the process**

Repeat steps 2, 3, and 4 until all the terms in the dividend have been considered.

**Step 6: Finalize the answer**

Once all the terms have been considered, we obtain the quotient and remainder. The quotient is the result obtained from step 2, and the remainder is the result obtained after all the divisions are completed.

**Example**

Let's consider an example to understand the long division method better.

Divide the polynomial P(x) = 3x^3 - 5x^2 + 2x - 4 by the polynomial Q(x) = x - 2.

Step 1: Arrange the polynomials
- P(x) = 3x^3 - 5x^2 + 2x - 4
- Q(x) = x - 2

Step 2: Divide the first term
- Divide 3x^3 by x, which gives 3x^2.
- Write the quotient 3x^2 above the line.

Step 3: Multiply and subtract
- Multiply (x - 2) by 3x^2, which gives 3x^3 - 6x^2.
- Subtract it from the dividend: (3x^3 - 5x^2 + 2x - 4) - (3x^3 - 6x^2) = x^2 + 2x - 4.

Step 4: Bring down the next term
- Bring down the next term, which is 2x, and write it next to x^2.
- The new dividend becomes x^2 + 2x - 4.

Step 5: Repeat the process
- Divide x^2 by x, which gives x.
- Write the quotient x above the line.

Step 6: Multiply and subtract
- Multiply (

You can find the answer by finding the zeros of the polynomial and then putting the value of zero in the given polynomial