Division of Polynomials To divide a polynomial by a monomial, we can divide each term by the monomial. Example           4x2 - 2x  - 3              4x2          - 2x             3                                     =               -                -                               5x                       5x             5x            5x                    4x             2          3         =                    -           -                                                                 5             5          5x   ExercisesDivide the polynomials     2x3 + 5x2 - 4                                            3x 7x4 - 3x2 + x - 2                                                  6x2 Recall how to perform long division.  We will divide 4321 by 6.  We see that we follow the steps: Write it in long division form. Determine what we need to multiply the quotient by to get the first term. Place that number on top of the long division sign. Multiply that number by the quotient and place the product below. Subtract Repeat the process until the degree of the difference is smaller than the degree of the quotient. Write as sum of the top numbers + remainder/quotient.   Example Divide         4321                                  6 Solution                720         6 | 4321                42        6 x 7  = 42                12       43 - 42  =  1 and drop down the 2                12       6 x 2  =  12                   01     12 - 12  =  0 and drop down the 1                    0      6 x 0  =  0                    1      1 - 0  =  1 To divide polynomials, we perform the same steps, except that there are x's involved.    Example Divide         x4 + 3x2 - 5                                             x2 + 4x Solution We first write in long division form Next decide what we need to multiply x2 by to get x4.  Since         (x2)(x2)  =  x4 we can write Next, we multiply x2 + 7x and x2. Now subtract to get and bring down the 3x2 to get We repeat this process until the degree of the remainder is less than the degree of the denominator. The final solution is                                   -76x + 5         x2 - 4x + 19 +                                                              x2 + 4x  Exercises Divide the polynomials.     3x2 + 5x + 7                                      x + 1 2x4 + x - 1                                   x2 + 3x + 1 Back to Math 152A Home Page