POLYDIV on the TI-83

The POLYDIV program divides one polynomial by another. The original form of the program is available on the TI web site. The version presented here has a trivial modification to that original. The POLYDIV program is available for download.

To demonstrate the use of POLYDIV on the TI-83, consider three problems, the first being

Figure 1	Figure 1 shows the screen on a TI-83 after we have pressed the key. This particular TI-83 had but two programs on it, and the one that we want is already selected. Therefore, we press to paste the name of the program onto the screen, as shown in Figure 2.
Figure 2	To actually start the program we press .
Figure 3	The POLYDIV program starts by asking us for the DIVIDEND LIST. This is a "list" that holds the coefficients of the dividend. In our case that list is {1,7,^–9}, corresponding to our dividend, 1x²+7x+^–9 Note that we needed to enter the coefficients as a list, enclosed in the braces. Then, the program asks for the the DIVISOR LIST. In this case that list is (1,8} corresponding to the divisor 1x+8 Figure 3 shows the screen display just before we press to move to Figure 4.
Figure 4	Here the program has processed the input data and it returns a list representing the quotient. In this example that list {1 ^–1} represents the polynomial 1x – 1 which is the quotient. The program is in a paused state in Figure 4 (note the array of dots at the upper right of the screen). We press the to continue the program on Figure 5.
Figure 5	The second line of output, {0 0 ^–1}, gives the remainder, or in this case, 0x²+0x–1 or, more simply, ^–1 The program is in a paused state. We press to continue the program.
Figure 6	The "Done" in Figure 6 indicates that the program has completed.

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 can re-start the program by pressing the key. Then we respond to the two prompts, giving the two lists of coefficients. After pressing , we have the result {1 ^–1 3} to indicate that the quotient is 1x²– 1x+3

Figure 8 We leave Figure 7 by pressing the key.
This displays the remainder, namely, ^–14. And pressing again ends the program.

Here is one more example:

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

Figure 9 Figure 9 shows the input phase of the program, along with the first output, the list {7 ^–6 ^–8 9} representing 7x³ – 6x² – 8x + 9

Figure 10 Figure 10 gives the rest of the output,
the remainder is ^–4

Figure 7	We can re-start the program by pressing the key. Then we respond to the two prompts, giving the two lists of coefficients. After pressing , we have the result {1 ^–1 3} to indicate that the quotient is 1x²– 1x+3
Figure 8	We leave Figure 7 by pressing the key. This displays the remainder, namely, ^–14. And pressing again ends the program.

Figure 9	Figure 9 shows the input phase of the program, along with the first output, the list {7 ^–6 ^–8 9} representing 7x³ – 6x² – 8x + 9
Figure 10	Figure 10 gives the rest of the output, the remainder is ^–4