How to Do Synthetic Division in Plain English

Synthetic division is a mathematical technique used to divide polynomials. It is a simpler and faster method than long division, which makes it a popular method in algebra. In this article, we will discuss how to do synthetic division in plain English.

What You Need to Know Before Starting

Before we dive into the steps for synthetic division, you need to know the following terms: Polynomial: A mathematical expression consisting of variables and coefficients, which can be combined using addition, subtraction, multiplication, and division. Degree: The highest power of the variable in a polynomial. For example, in the polynomial 4x^3 + 2x^2 - 5x + 1, the degree is 3. Divisor: The polynomial used to divide another polynomial. Remainder: The leftover value after the polynomial division.

Steps to Perform Synthetic Division

Follow these steps to perform synthetic division: Step 1: Write the polynomial in standard form. For example, let's say we have to divide 2x^3 - 5x^2 + 3x - 7 by x - 2. We will write the polynomial in the standard form as follows:

2 | 2 -5 3 -7

            0 4 -2 10
Note: The divisor x - 2 is written as 2 because the opposite of 2 is used in the calculation. Step 2: Write the coefficients of the polynomial in the first row of the synthetic division table. The first row should contain the coefficients of the polynomial in the order of decreasing degrees. For example, in our case, the first row will be:

| 2 -5 3 -7

Step 3: Write the root of the divisor in the second row of the synthetic division table. The second row should contain the root of the divisor. In our case, the root is 2, so the second row will be:

2 | 2 -5 3 -7

            |

          2

Step 4: Multiply the root with the first coefficient of the polynomial and write the result below the first coefficient. In our case, we will multiply 2 with 2 and write the result below -5, which is 4:

| 2 -5 3 -7

            |

          2

            4 Step 5: Add the result to the second coefficient of the polynomial and write the result below the second coefficient. In our case, we will add 4 to -5 and write the result below 3, which is -1:

| 2 -5 3 -7

            |

          2

            4 -1 Step 6: Multiply the root with the previous result and repeat the process until you reach the last coefficient. In our case, we will multiply 2 with -1 and write the result below -7, which is -14:

| 2 -5 3 -7

            |

          2

            4 -1 -14 Step 7: Write the final result in the last row of the synthetic division table. The last row will contain the coefficients of the quotient and the remainder. In our case, the last row will be:

| 2 -5 3 -7

            |

          2

            4 -1 -14

         2x^2 - x - 7 + (-14)/(x-2)

Note: The quotient is 2x^2 - x - 7, and the remainder is -14/(x-2).

FAQs

Here are some frequently asked questions about synthetic division:

Question	Answer
Can I use synthetic division for all polynomial divisions?	No, synthetic division can only be used when dividing by a linear polynomial of the form x-a.
Can I use synthetic division if the divisor has a degree greater than 1?	No, synthetic division only works when dividing by a linear polynomial.
What is the advantage of using synthetic division over long division?	Synthetic division is a simpler and faster method than long division, which makes it a popular method in algebra.

Conclusion

Synthetic division is a useful technique to divide polynomials, especially when dividing by a linear polynomial of the form x-a. In this article, we discussed the steps to perform synthetic division in a simple and easy-to-understand manner. We also saw how to use synthetic division to find the quotient and remainder of a polynomial division. By following the steps outlined in this article, you can easily perform synthetic division for your own polynomial problems. Remember that practice is key to mastering any mathematical technique, so try to solve as many synthetic division problems as you can to become proficient in it. With enough practice, you will be able to use synthetic division confidently and quickly. If you have any further questions or doubts about synthetic division, feel free to consult your math teacher or tutor. You can also refer to online resources and practice problems to improve your skills. Good luck with your math journey! Thank you for reading this article. If you found it helpful, don't forget to check out our other articles on math and science topics. We hope to see you soon with more interesting articles. Goodbye!

Share :