Using synthetic division on polynomials of up to degree 6, a user can look at the values in H4 and H8 to determine if a number between Trial1 and Trial2 crosses the x-axis, there is a solution to the equation between the trial values. Occasionally, you may find an exact solution, this occurs when either H4 or H8 is 0.
f(x) is entered into the input box in any order, the applet will fill the columns for you. Enter the two test values into Trial1 and Trial2.
If you enter f(x) = x³ - 2 x² - x + 1 in the input box, the applet will enter {1, -2, -1, 1} in rows 2 and 6, then type Trial values 2 in A2 and 3 in A6. If the values in H4 and H7 have different signs, then there is a solution between 2 and 3. A note comes up stating you have a solution between 2 and 3.
To preserve the formulas in the cells, be sure to use Reset Button on the screen. Do not write in any cell other than the light red ones, there are formulas in them.

This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers as a worksheet to be completed for a grade.