LONG+AND+SYNTHETIC+DIVISION

Synthetic division ** Synthetic division is a method of polynomial division by a linear factor. The change of sign of //b// when dividing by (//x// + //b//) (i.e. −//b// is written to the left of the bar rather than //b//) allows us to do additions rather than subtractions that are found in regular long division. This reduces the chance for error when the division is done by hand.

Example of synthetic step by step

**Long Division**:

Set up the division: For the moment, ignore the other terms and look at the //x//  and the  //x//2. What do you have to multiply  //x//   by, to get   //x//2   ? An  //x//   ; put this on top: Take that //x//  , and multiply it through the   //x// + 1. First, you multiply  //x//   on the   //x//   ; carry the   //x//2   underneath: Then multiply the //x//   on the   1   ; carry the   1//x//   underneath Draw the equals bar. To subtract, //change all the signs// in the second line... ...and add down. The first term will cancel out: Remember to carry down that last term from the dividend: Now look at the //x//   from the divisor and the   –10//x//   from the bottom line in the division. What do you have to multiply  //x//   by to get   –10//x//   ? A minus ten; put this on top: Now multiply the –10   on the   //x//  , and carry the   –10//x//   to the bottom: ...and multiply the –10   on the   1  , and carry the   –10   to the bottom Draw the equals bar, and //change the signs// on all the terms in the bottom row: Then add down: The Solution would be: x-10