POLY3 on the TI-86

The POLY3 program does a number of things with polynomials. On this page we are interested in having the POLY3 program divide two polynomials. The program is available for the TI-85 and for the TI-86. The two programs are identical and their use is identical. The original form of the program is available on the TI web site. The POLY3 program for the TI-85 is available for download, as is the POLY3 program for the TI-86.

To demonstrate the use of POLY3 on the TI-85 and TI-86, consider three problems, the first being

Figure 1	Figure 1 illustrates the screen after we have opened the PRGM menu, via the key, selected the NAMES option via the key, used the key to shift the menu until it displays the POLY3 item. On this calculator that selection appears in the second position. To complete Figure 1, we press the key to paste the name of the program onto the screen.
Figure 2	Then we press to start the program. The program has started in Figure 2, but the only thing that has happened is that the menu has changed. In fact, the only thing that we can do is to select one of the options given in the menu. We want to "input" our problem. Therefore , we press to move to the input phase.
Figure 3	The input phase changes the menu again. Now we need to decide among these menu items. We want to enter a list for the dividend. We will put that list into {P1}. Therefore, we press to input the {P1} list.
Figure 4	The program prompts us for the list of values to put into {P1}. The menu has disappeared. We need to enter the list. However, to do this we need to be able to type the brace, {. That character is not on the keyboard. We can find the { and the } on the LIST menu. We press to open that menu, shown at the bottom of Figure 5.
Figure 5	Now we can use the menu ites to formulate our list of coefficients for the dividend, namely, {1,7,^–9} When we have completed the entry of the list, we press to continue.
Figure 6	The program responds by displaying the earlier menu. We will want to enter the second polynomial, {P2}, to hold the coefficients of the divisor. Therefore, we press .
Figure 7	Again we want to enter a LIST, and again we need to open the LIST menu so that we have access to the { and } characters. We press to open the LIST menu, shown at the bottom of Figure 8.
Figure 8	In Figure 8 we have used the menu items to help enter the list that is to be assigned to {P1}. Then we hit the key to move to Figure 8a.
Figure 8a	We are done with our input phase. We want to return to the earlier menu in the POLY3 program. Therefore, we presss the key to select the menu option, which will take us back to the earlier menu, as shown at the bottom of Figure 9.
Figure 9	Our choices are limited to the items in the menu. We have already input the lists that represent the two polynomials. Press to select the ALG option. This will open a new menu, shown at the bottom of Figure 10.
Figure 10	The menu gives us the options of *P1P2 to get the product of the polynomials P1/P2 to get the quotient of the polynomials P1^P to raise P1 to some power P1=0** to find the zeros of P1 to return to the previous menu. Choose to find the quotient.
Figure 11	The program responds with the quotient, given as a list of coeeficients. Thus, {1 ^–1 represents 1x – 1 The program is in a paused condition. Press to continue.
Figure 12	The program has gone on to give us the remainder, again as a list of coefficients. In this case that remainder is just the constant, ^–1. Note that the program is in a paused condition again. Press to continue the program.
Figure 13	In Figure 13 the program has returned to give us the options of the menu at the bottom of the screen. We are done with this problem. Therefore, press to return to the previous menu.
Figure 14	The options of this menu would allow us to quit if we are done with the program, or to enter new values if we want to do another polynomial division.

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 15 Our first step will be to enter the two polynomials. To move to Figure 15 we have pressed to onpen the INPUT menu. Now we can press to allow us to enter the LIST of coefficients for the DIVISOR.

Figure 16 In Figure 16 the program is prompting us for the list of coefficients. As before, we need to open the LIST menu in order to make the braces, { and } available to us. Press to open that menu, shown at the bottom of Figure 17.

Figure 17 To produce Figure 17 we have entered the list of coefficients for {P1}, pressed to accept that list and return to the INPUT menu, chosen to enter {p2} from that menu, opened the LIST menu again, and entered the coefficients for the DIVISOR list.

Figure 18 Press the key to accept that list and return to the INPUT menu, shown in Figure 18. Then press to return to the previous menu, shown at the bottom of Figure 19.

Figure 19 We will use the key to select the ALG menu option, and move to Figure 20.

Figure 20 Figure 20 represents the result of having asked for the P1/P2 option, getting the quotient list, pressing to continue, and having the program display the remainder list. According to Figure 20, the quootient is 1x² – 1x + 3 and the remainder is the constant ^–14.

Here is one more example:

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

Figure 21 Figure 21 shows the result of moving through the program until we have entered the two polynomials by giving the program the two lists of coefficients.

Figure 22 Once the input phases has been completed, we move through the menus to find the menu item requesting the program to compute the quotient.

Figure 23 Figure 23 shows the resulting answers. In addition, to generate Figure 23 we have moved though the menus to return to the main menu. This will allow us to demonstrate terminating the program by pressing the key to select the QUIT menu option.

Figure 24 The Done in Figure 24 indicates that we have terminated the program.

Figure 15	Our first step will be to enter the two polynomials. To move to Figure 15 we have pressed to onpen the INPUT menu. Now we can press to allow us to enter the LIST of coefficients for the DIVISOR.
Figure 16	In Figure 16 the program is prompting us for the list of coefficients. As before, we need to open the LIST menu in order to make the braces, { and } available to us. Press to open that menu, shown at the bottom of Figure 17.
Figure 17	To produce Figure 17 we have entered the list of coefficients for {P1}, pressed to accept that list and return to the INPUT menu, chosen to enter {p2} from that menu, opened the LIST menu again, and entered the coefficients for the DIVISOR list.
Figure 18	Press the key to accept that list and return to the INPUT menu, shown in Figure 18. Then press to return to the previous menu, shown at the bottom of Figure 19.
Figure 19	We will use the key to select the ALG menu option, and move to Figure 20.
Figure 20	Figure 20 represents the result of having asked for the P1/P2 option, getting the quotient list, pressing to continue, and having the program display the remainder list. According to Figure 20, the quootient is 1x² – 1x + 3 and the remainder is the constant ^–14.

Figure 21	Figure 21 shows the result of moving through the program until we have entered the two polynomials by giving the program the two lists of coefficients.
Figure 22	Once the input phases has been completed, we move through the menus to find the menu item requesting the program to compute the quotient.
Figure 23	Figure 23 shows the resulting answers. In addition, to generate Figure 23 we have moved though the menus to return to the main menu. This will allow us to demonstrate terminating the program by pressing the key to select the QUIT menu option.
Figure 24	The Done in Figure 24 indicates that we have terminated the program.