How to Do Algebra Division?

Algebraic division, specifically polynomial long division, is a method for dividing polynomials. It's similar to long division with numbers. Here's how to perform it:

Steps to Perform Algebraic Long Division

1. Set up the long division: Arrange both the dividend (polynomial being divided) and the divisor (polynomial dividing) in descending order of exponents. Leave space for missing terms (terms with a coefficient of zero) in the dividend. This is crucial for accurate subtraction in later steps. [Reference: wtamu.edu - Step 1]

2. Divide the leading terms: Divide the first term of the dividend by the first term of the divisor. This gives you the first term of your quotient.

3. Multiply and subtract: Multiply the term obtained in step 2 by the entire divisor. Subtract this result from the corresponding terms in the dividend.

4. Repeat the process: Bring down the next term of the dividend and repeat steps 2 and 3. Continue this process until you have no more terms to bring down.

5. Interpret the result: The final result consists of the quotient (the result of the division) and the remainder (any remaining terms after the division process is complete). If the remainder is zero, the divisor divides the dividend evenly. [Reference: wtamu.edu - Steps 2-5]

Example

Let's divide (3x² + 5x - 2) by (x + 2):

1. Setup:

      x + 2 | 3x² + 5x - 2

2. Divide leading terms: 3x²/x = 3x. This is the first term of the quotient.

      3x
x + 2 | 3x² + 5x - 2

3. Multiply and subtract: 3x * (x + 2) = 3x² + 6x. Subtracting this from the dividend gives:

      3x
x + 2 | 3x² + 5x - 2
      - (3x² + 6x)
      --------------
              -x - 2

4. Repeat: Bring down -2. Divide -x by x to get -1. This is the next term of our quotient.

      3x - 1
x + 2 | 3x² + 5x - 2
      - (3x² + 6x)
      --------------
              -x - 2
              - (-x -2)
              ---------
                  0

5. Result: The quotient is 3x - 1, and the remainder is 0. Therefore, (3x² + 5x - 2) / (x + 2) = 3x -1.

Resources for Further Learning

• WTAMU Math Lab: Long Division: Step-by-step guide to polynomial long division.
• Corbettmaths: Algebraic Long Division: Video tutorial explaining the process.