POLYDIV1 on the TI-83

The POLYDIV1 program for the TI-83 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 as POLYDIV1.) In order to show all of the work for the problem, the TI-83 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 POLYDIV1 on the right.

As we can see from the illustration above, the POLYDIV1 program produces all of the numbers associated with the traditional polynomial division algorithm. This page will demonstrate the use of the POLYDIV1 program on the TI-83. We will start by doing the problem illustrated above.

Figure 1 Figure 1 is the result of pressing the key to open the PROGRAM menu, and then using the key to move the highlight to the POLYDIV1 name. Once the POLYDIV1 program has been selected, we press the key to move to Figure 2.

Figure 2 The actions in Figure 1 pasted the command prgmPOLYDIV1 onto the screen. Now we are ready to press the key to start the program.

Figure 3 The POLYDIV1 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 3.
We press the key to accept that list and move to Figure 4.

Figure 4 The POLYDIV1 program displays the initial matrix in Figure 4. 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 5.

Figure 5 In Figure 5 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. For this problem we can see all of the answer on the screen. Therefore, we do not need to look at any hidden values. We press to continue, and move to Figure 6.

Figure 6 Once the program has reached the end of the division, the POLYDIV1 program displays the menu shown in Figure 6. This allows us to
start a new problem by pressing 0
end the POLYDIV1 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 7 We left Figure 6 by pressing the key to tell the calculator that we have a new problem to do. The POLYDIV1 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 7 shows that list as {1,2,0,^–5}

Figure 8 Pressing moves the program from Figure 7 to Figure 8. 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 9.

Figure 9 Figure 9 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 10.

Figure 10 In the earlier Figures we could see all that we needed to see on the screen. Now, in Figure 10, we can see some of the values but we are missing the rightmost numbers and the bottom numbers. Because the program is paused, we can use the cursor keys to move around on the screen. For example, we can press the key to move to the right, as seen in Figure 11.

Figure 11 Figure 11 displays the right side of the matrix. We can use the key to move down to see the bottom of the matrix, as it appears in Figure 12.

Figure 12 Now that we can see the bottom of the matrix we note that 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 13 In Figure 13 we have pressed to ask for a new problem, and we have entered both the DIVISOR LIST and the DIVIDEND LIST.

Figure 14 Press to move from Figure 13 to Figure 14. Here we can see the matrix after the first step of the algorithm. Unfortunately, we can only see the left side of the matrix. We press the key to move the display to the right so that we can see the rest of the DIVIDEND in Figure 15.

Figure 15 Having seen the entire DIVIDEND, we press to continue the program.

Figure 16 Figure 16 shows the matrix after the second step. Note that we can not even see, in Figure 16, the second coefficient of the quotient.

Figure 17 We use the key to shift the display to the right to give Figure 17.

Figure 18 To move from Figure 17 to Figure 18 we press to take the next step in the algorithm and then we use the key to shift the display to the right. Then, we do another to move to Figure 19.

Figure 19 At this point all of the updates from the program are happenning in matrix cells that are off the screen. As it turns out, at this point we are really done with the problem, but we do not know it. We press one more time to move to Figure 20.

Figure 20 Figure 20 shows us the bottom of the matrix, and the menu options. We need to go back to see to top right of the matrix to see the rest of the quotient, and the bottom right of the matrix, to see the remainder. Therefore, we select option 2 to show the matrix again. When we follow this by pressing the matrix will be displayed again. Then we can use teh key to shift the display to the right, as shown in Figure 21.

Figure 21 Figure 21 shows us the rest of the quotient. We can press the key to shift the display down to show us the remainder, as in Figure 22.

Figure 22 Finally, Figure 22 shows us the remainder. If we were to follow this by presssing the key, the program would take us back to the display in Figure 20. At that point we could choose one of the other options.

Figure 1	Figure 1 is the result of pressing the key to open the PROGRAM menu, and then using the key to move the highlight to the POLYDIV1 name. Once the POLYDIV1 program has been selected, we press the key to move to Figure 2.
Figure 2	The actions in Figure 1 pasted the command prgmPOLYDIV1 onto the screen. Now we are ready to press the key to start the program.
Figure 3	The POLYDIV1 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 3. We press the key to accept that list and move to Figure 4.
Figure 4	The POLYDIV1 program displays the initial matrix in Figure 4. 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 5.
Figure 5	In Figure 5 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. For this problem we can see all of the answer on the screen. Therefore, we do not need to look at any hidden values. We press to continue, and move to Figure 6.
Figure 6	Once the program has reached the end of the division, the POLYDIV1 program displays the menu shown in Figure 6. This allows us to start a new problem by pressing 0 end the POLYDIV1 program by pressing 1 show the answer to the last problem by pressing 2.

Figure 7	We left Figure 6 by pressing the key to tell the calculator that we have a new problem to do. The POLYDIV1 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 7 shows that list as {1,2,0,^–5}
Figure 8	Pressing moves the program from Figure 7 to Figure 8. 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 9.
Figure 9	Figure 9 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 10.
Figure 10	In the earlier Figures we could see all that we needed to see on the screen. Now, in Figure 10, we can see some of the values but we are missing the rightmost numbers and the bottom numbers. Because the program is paused, we can use the cursor keys to move around on the screen. For example, we can press the key to move to the right, as seen in Figure 11.
Figure 11	Figure 11 displays the right side of the matrix. We can use the key to move down to see the bottom of the matrix, as it appears in Figure 12.
Figure 12	Now that we can see the bottom of the matrix we note that 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 13	In Figure 13 we have pressed to ask for a new problem, and we have entered both the DIVISOR LIST and the DIVIDEND LIST.
Figure 14	Press to move from Figure 13 to Figure 14. Here we can see the matrix after the first step of the algorithm. Unfortunately, we can only see the left side of the matrix. We press the key to move the display to the right so that we can see the rest of the DIVIDEND in Figure 15.
Figure 15	Having seen the entire DIVIDEND, we press to continue the program.
Figure 16	Figure 16 shows the matrix after the second step. Note that we can not even see, in Figure 16, the second coefficient of the quotient.
Figure 17	We use the key to shift the display to the right to give Figure 17.
Figure 18	To move from Figure 17 to Figure 18 we press to take the next step in the algorithm and then we use the key to shift the display to the right. Then, we do another to move to Figure 19.
Figure 19	At this point all of the updates from the program are happenning in matrix cells that are off the screen. As it turns out, at this point we are really done with the problem, but we do not know it. We press one more time to move to Figure 20.
Figure 20	Figure 20 shows us the bottom of the matrix, and the menu options. We need to go back to see to top right of the matrix to see the rest of the quotient, and the bottom right of the matrix, to see the remainder. Therefore, we select option 2 to show the matrix again. When we follow this by pressing the matrix will be displayed again. Then we can use teh key to shift the display to the right, as shown in Figure 21.
Figure 21	Figure 21 shows us the rest of the quotient. We can press the key to shift the display down to show us the remainder, as in Figure 22.
Figure 22	Finally, Figure 22 shows us the remainder. If we were to follow this by presssing the key, the program would take us back to the display in Figure 20. At that point we could choose one of the other options.