Synthetic Division (Extended Version)
- Author:
- Auston B Cron
- Topic:
- Polynomial Functions
This applet will enable you to learn synthetic division with ease and efficiency. Polynomials of up to degree 6 can be entered, the program will do the arithmetic, you need to learn how to do this on your own. Have fun!!
Enter f(x) into the input box, then enter you first divisor under Trial1. If you get a zero for the remainder of the first divisor or the actual remaider, you then can add a second divisor in A6 under Trial2, repeat until you can go no longer. If you need assistance for this, see this lesson. If your polynomial has degree 2, the quadratic formula or factoring will be more efficient.
If any row has values only the last two columns, you can solve the linear equation for its value of x by setting a x + c = 0.
To determine the values for the divisors in the A column, use the pq estimates of these values. 'p' represents all the factors of the constant term. 'q' represents all factors of the leading coefficient. See this lesson for assistance.
To preserve the formulae in the cells, be sure to type only in the blue or pink boxes. A Reset button will allow you to start an new expression. Use the recycle icon on the upper right of the graphic screen if you need to restore formulae. Sample1 show a fully factorable expression; Sample2 shows a partially factorable expression.
Warning: This applet does not solve all Synthetic Division problems, it will not solve problems with complex roots. It is a tool to help you to learn to do synthetic division yourself; with repeated use you may be able to find constant factors.