Division of Polynomials
Division of polynomials is very similar to the long division you did in middle school. Consider the process of dividing 5249 by 321:
Because 103 is less than the divisor 321, we have that the quotient is 16 and the remainder is 113. That is, 5249 ÷ 321 is
Dividing polynomials is a similar process, but there are places where you will need to be careful. Read through each of the examples that follow. After you have read each problem, copy it onto a piece of paper and see if you can arrive at the correct answer. Be sure to be careful when doing the subtraction.
We find that 6x3 − 7x2 − 47x − 36 by 3x + 4 = 2x2 − 5x − 9.
Finishing the problem, you see that
This problem has a remainder, so the solution is
Example: Divide 8r3 − 4r2 + 19 by 2r + 3.
Note that there is no term between −4r2 and 19 containing an r. We insert a placeholder, using a 0 for a coefficient. The steps for solving the problem remain the same.
8r3 − 4r2 + 19 divided by 2r + 3 is
Divisors do not always have to be binomials.