polydiv on the TI-89

The polydiv program for the TI-89 and the TI-92 Plus does division of polynomials, giving not only the quotient and the remainder, but also all of the steps along the way. (The program can be downloaded for the TI-89 as polydiv for the TI-89, and as polydiv for the TI-92 Plus. Note that there is a version for the TI-92 at polydiv for the TI-92 but the TI-92 does not seem to scroll the Program IO window.) This page uses the TI-89 version of the program, recognizing that the TI-92 will perform the same steps, and that the screen will be larger.

In order to show all of the work for the problem, the TI-89 uses a matrix to hold the divisor, the dividend, the quotient, the remainder, and all of the rest of the computations. For example consider the problem on the left, and its representation in polydiv on the right.

As we can see from the illustration above, the polydiv program produces all of the numbers associated with the traditional polynomial division algorithm. We will start the demonstration of the polydiv program by doing the problem illustrated above.

Figure 1 Figure 1 is the result of pressing the keys to open the List of Variables. The TI-89 responds with a list of all variables. We use the key to move to successive variables that start with the letter "P", remembering that the TI-89 is not case-sensitive. We could also use the the key to move the highlight. In any case, Figure 1 demonstrates that we have moved to highlight the polydiv name. Once the polydiv program has been selected, we press the key to move to Figure 2.
Figure 2 The actions of Figure 1 have pasted the name of our program, polydiv, into the command line of the calculator. In addition, the calculator has appended the required left parenthesis. There are no parameters for the polydiv program. Therefore, we can complete the command by supplying the matching right parenthesis.

Figure 3 In Figure 3 we have completed the command by pressing the key.
Now to begin the program we press the key.

Figure 4 The polydiv program prompts us for the DIVISOR LIST. We respond by entering {1,8} representing 1x+8 then we press the key to have the calculator accept our list. Then the program moves on to prompt for the DIVIDEND LIST. We respond with {1,7,^–9} representing 1x²+7x–9 This is the condition of the calculator in Figure 4.
We press the key to accept that list and move to Figure 5.

Figure 5 The polydiv program displays the initial matrix in Figure 5. At this point the initial division has been done. That is, the program reflects the problem at the stage of completing the initial division, namely, The program is in a "paused" condition to allow us to inspect the matrix of values. We press to continue the division and move to Figure 6.

Figure 6 In Figure 6 the program has taken another step, determining the second coefficient in the quotient. In this case, that is really all that there is to the problem. Again the program is in a paused state so that we can move around in the matrix if need be. And, indeed, we can not see the bottom row of the matrix. Therefore, we press the key to shift the display to that of Figure 7.

Figure 7 Here we see the rest of the matrix. Having seen all of the problem we press to continue, and move to Figure 8.

Figure 8 Once the program has reached the end of the division, the polydiv program displays the menu shown in Figure 8. This allows us to
start a new problem by pressing 0
end the polydiv program by pressing 1
show the answer to the last problem by pressing 2.

Let us look at another problem, namely,

Here the DIVIDEND LIST will be {1,2,0,^–5} with {1,3} as the DIVISOR LIST.

Figure 9 We left Figure 8 by pressing the key to tell the calculator that we have a new problem to do. The polydiv program again asks for the DIVISOR LIST, to which we respond with {1,3} and then . The program then asks for the DIVIDEND LIST. Figure 9 shows that list as {1,2,0,^–5}

Figure 10 Pressing moves the program from Figure 9 to Figure 10. The program is paused. We can examine the output and note that the first coefficient of the quotient is 1. Press to move to Figure 11.

Figure 11 Figure 11 shows the calculator display after the second cycle of the division algorithm. The second coefficient of the quotient has been computed to be "^–1" and the corresponding portion of the division algorithm has been completed. Press to move to Figure 12.

Figure 12 Again, we can use the key to move the display down to show the rest of the matrix, as it appears in Figure 12.
Press to move to Figure 13.

Figure 13 Figure 13 shows the top portion of the final matrix. Again, we can use the key to move the display down to show the rest of the matrix, as it appears in Figure 14.

Figure 14 Here is the lower portion of the matrix.
The problem is done. If we press the ENTER the program will display the options to do a new problem, quit, or re-display the current matrix.

Here is one more example:

Now the DIVIDEND LIST will be {14,^–47,14,58,^–49} with {2,^–5} as the DIVISOR LIST.

Figure 15 In Figure 15 we have pressed to ask for a new problem, and we have entered both the DIVISOR LIST and the DIVIDEND LIST.

Figure 16 Press to move from Figure 15 to Figure 16. Here we can see the matrix after the first step of the algorithm.

Figure 17 Press to move from Figure 16 to Figure 17. Here we can see the matrix after the second step of the algorithm.

Figure 18 Press to move from Figure 17 to Figure 18. Here we can see the matrix after the third step of the algorithm. As in the earlier example, we can not see the bottom portion of the matrix. We press the key to move the display down so that we can see the rest of the matrix in Figure 19.

Figure 19 In Figure 19 we can see the rest of the matrix. We press the key to continue the algorithm.

Figure 20 Now we can see the matrix after the fourth and final step. However, now we are missing both the bottom of the matrix and the right side of the matrix. We can use both the key and the key to move down and to the right to see the rest of the matrix, as shown in Figure 21.

Figure 21 Figure 21 shows the rest of the matrix. We can press the key to return to our menu.

Figure 22 In Figure 22 we see the conclusion of the program. We have responded to the menu by pressing the key and the key. The TI-89 remains in the Program IO screen that is Figure 21. We would have to press the key to return to the main screen.

Figure 1	Figure 1 is the result of pressing the keys to open the List of Variables. The TI-89 responds with a list of all variables. We use the key to move to successive variables that start with the letter "P", remembering that the TI-89 is not case-sensitive. We could also use the the key to move the highlight. In any case, Figure 1 demonstrates that we have moved to highlight the polydiv name. Once the polydiv program has been selected, we press the key to move to Figure 2.
Figure 2	The actions of Figure 1 have pasted the name of our program, polydiv, into the command line of the calculator. In addition, the calculator has appended the required left parenthesis. There are no parameters for the polydiv program. Therefore, we can complete the command by supplying the matching right parenthesis.
Figure 3	In Figure 3 we have completed the command by pressing the key. Now to begin the program we press the key.
Figure 4	The polydiv program prompts us for the DIVISOR LIST. We respond by entering {1,8} representing 1x+8 then we press the key to have the calculator accept our list. Then the program moves on to prompt for the DIVIDEND LIST. We respond with {1,7,^–9} representing 1x²+7x–9 This is the condition of the calculator in Figure 4. We press the key to accept that list and move to Figure 5.
Figure 5	The polydiv program displays the initial matrix in Figure 5. At this point the initial division has been done. That is, the program reflects the problem at the stage of completing the initial division, namely, The program is in a "paused" condition to allow us to inspect the matrix of values. We press to continue the division and move to Figure 6.
Figure 6	In Figure 6 the program has taken another step, determining the second coefficient in the quotient. In this case, that is really all that there is to the problem. Again the program is in a paused state so that we can move around in the matrix if need be. And, indeed, we can not see the bottom row of the matrix. Therefore, we press the key to shift the display to that of Figure 7.
Figure 7	Here we see the rest of the matrix. Having seen all of the problem we press to continue, and move to Figure 8.
Figure 8	Once the program has reached the end of the division, the polydiv program displays the menu shown in Figure 8. This allows us to start a new problem by pressing 0 end the polydiv program by pressing 1 show the answer to the last problem by pressing 2.

Figure 9	We left Figure 8 by pressing the key to tell the calculator that we have a new problem to do. The polydiv program again asks for the DIVISOR LIST, to which we respond with {1,3} and then . The program then asks for the DIVIDEND LIST. Figure 9 shows that list as {1,2,0,^–5}
Figure 10	Pressing moves the program from Figure 9 to Figure 10. The program is paused. We can examine the output and note that the first coefficient of the quotient is 1. Press to move to Figure 11.
Figure 11	Figure 11 shows the calculator display after the second cycle of the division algorithm. The second coefficient of the quotient has been computed to be "^–1" and the corresponding portion of the division algorithm has been completed. Press to move to Figure 12.
Figure 12	Again, we can use the key to move the display down to show the rest of the matrix, as it appears in Figure 12. Press to move to Figure 13.
Figure 13	Figure 13 shows the top portion of the final matrix. Again, we can use the key to move the display down to show the rest of the matrix, as it appears in Figure 14.
Figure 14	Here is the lower portion of the matrix. The problem is done. If we press the ENTER the program will display the options to do a new problem, quit, or re-display the current matrix.

Figure 15	In Figure 15 we have pressed to ask for a new problem, and we have entered both the DIVISOR LIST and the DIVIDEND LIST.
Figure 16	Press to move from Figure 15 to Figure 16. Here we can see the matrix after the first step of the algorithm.
Figure 17	Press to move from Figure 16 to Figure 17. Here we can see the matrix after the second step of the algorithm.
Figure 18	Press to move from Figure 17 to Figure 18. Here we can see the matrix after the third step of the algorithm. As in the earlier example, we can not see the bottom portion of the matrix. We press the key to move the display down so that we can see the rest of the matrix in Figure 19.
Figure 19	In Figure 19 we can see the rest of the matrix. We press the key to continue the algorithm.
Figure 20	Now we can see the matrix after the fourth and final step. However, now we are missing both the bottom of the matrix and the right side of the matrix. We can use both the key and the key to move down and to the right to see the rest of the matrix, as shown in Figure 21.
Figure 21	Figure 21 shows the rest of the matrix. We can press the key to return to our menu.
Figure 22	In Figure 22 we see the conclusion of the program. We have responded to the menu by pressing the key and the key. The TI-89 remains in the Program IO screen that is Figure 21. We would have to press the key to return to the main screen.