Synthetic+Division

=Synthetic Division =

Definition:
- A simplified method for dividing a polynomial by another polynomial of the first degree by writing down only the coefficients of the several powers of the variable and changing the sign of the constant term in the divisor so as to replace the usual subtractions by additions
 * The definition above is provided by Merriam Webster: [|Synthetic Division 1] **

- A shortcut method for dividing a polynomial by a linear factor of the form //x-a//. It can be used in place of the standard long division algorithm. This method reduces the polynomial and the linear factor into a set of numeric values. After these values are processed, the resulting set of numeric outputs is used to construct the polynomial quotient and the polynomial remainder.
 * The definition above is provided by Math World: [|Synthetic Division 2]**

- A shorthand for long division, when one of the factors is linear.
 * The Definition above is provided by PlanetMath: [|Synthetic Division 3] **

Links that will assist you in problems regarding synthetic division:
1. [|The Basics of Synthetic Division] 2. [|Step-By-Step Process of Synthetic Division] 3. [|Example Problem]


 * ﻿Still having trouble? Here is an EXAMPLE PROBLEM to help you out: **
 * **Bring down the 1. [[image:http://www.helpalgebra.com/articles/images/syn10.gif width="230" height="78"]]**
 * **Multiply it by the -3 to get -3. **
 * **Add 1+-3 to get -2. **
 * **Multiply -2 times -3 to get 6. **
 * **Add 2 plus 6 to get 8. **
 * **Multiply 8 times -3 to get -24. **
 * **Add 5 plus -24 to get -19. **
 * **<span style="color: #7f0200; font-family: 'Trebuchet MS',Helvetica,sans-serif;">Multiply -19 times -3 to get 57. **
 * **<span style="color: #02007f; font-family: 'Trebuchet MS',Helvetica,sans-serif;">Add -3 plus 57 to get 54. **
 * **<span style="color: #7f0200; font-family: 'Trebuchet MS',Helvetica,sans-serif;">Multiply 54 times -3 to get -162. **
 * **<span style="color: #000080; font-family: 'Trebuchet MS',Helvetica,sans-serif;">Add 6 plus -162 to get -156. * **
 * **<span style="color: #ff0006; font-family: 'Trebuchet MS',Helvetica,sans-serif;">THE FINAL ANSWER: x4-2x3+8x2-19x+54 R -156* **

<span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">Now, let's test your knowledge of synthetic division! Take this Multiple Choice Test! **GOOD LUCK :)**

<span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">1.) Synthetic Division is used to calculate "what"? <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">A. the product of 2 polynomials <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">B. the divisor in a rational expression <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">C. the quotient of 2 polynomials <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">D. It does not calculate anything

<span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">2.) Perform the following synthetic division: 10y4 - 72y3 - 56y2 - 61y - 24 ÷ y - 8 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">A. 18y3 + 18y2 + 18y + 13 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">B. 10y3 + 22y2 + 22y + 17 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">C. 10y3 + 8y2 + 8y + 3 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">D. 10y3 + 12y2 + 12y + 7

<span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">3.) Perform the following synthetic division: 6m5 - 14m4 - 31m3 - 34m2 - 32 ÷ m - 4 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">A. 14m4 + 16m3 + 15m2 + 8m + 14 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">B. 6m4 + 15m3 + 14m2 + 7m + 13 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">C. 6m4 + 10m3 + 9m2 + 2m + 8 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">D. 6m4 + 17m3 + 16m2 + 9m + 15

<span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">4.) Perform the following synthetic division: 4g5 - 29g4 - 61g3 - 11g2 - 59g - 36 ÷ g - 9 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">A. 4g4 + 7g3 + 2g2 + 7g + 4 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">B. 4g4 - 11g3 - 16g2 - 11g - 14 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">C. -20g4 + g3 - 4g2 + g - 2 <span style="color: #0000ff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">D. 4g4 - 20g3 - 25g2 - 20g - 23


 * <span style="color: #ff00d4; font-family: 'Trebuchet MS',Helvetica,sans-serif;">STILL HAVING TROUBLE? WATCH THIS PODCAST FOR SYNTHETIC DIVISION: **
 * <span style="color: #ff00d4; font-family: 'Trebuchet MS',Helvetica,sans-serif;">[|Podcast] **