Question 74623
<pre><font size = 4><b>Please can you give me a step by step solution of the following 
long division of polynominals question:
3x^4+4x^3-2x^2+8 divided by 2x^3-18x+2x^2-18.

This isn't step-by-step, but if you can't follow it at all
then you need to learn the procedure from simpler examples.
This is too advanced a problem from which to be learning 
the procedure for the first time.

The dividend polynomial 3x<sup>4</sup> + 4x<sup>3</sup> - 2x<sup>2</sup> + 8 is in order of
descending powers of x but it has a missing term in x. So 
we need to insert a place-holder of + 0x and write it as:

3x<sup>4</sup> + 4x<sup>3</sup> - 2x<sup>2</sup> + 0x + 8

The divisor polynomial 2x3 - 18x + 2x2 - 18 is not in
order of descending powers of x so we write it as
2x<sup>3</sup> + 2x<sup>2</sup> - 18x - 18

                                <u>                    1.5x + .5</u>
            2x<sup>3</sup> + 2x<sup>2</sup> - 18x - 18) 3x<sup>4</sup> + 4x<sup>3</sup> -  2x<sup>2</sup> +   0x + 8
                                  <u>3x<sup>4</sup> + 3x<sup>3</sup> - 27x<sup>2</sup> -  27x</u> 
                                        x<sup>3</sup> + 25x<sup>2</sup> +  27x +  8
                                        <u>x<sup>3</sup> +   x<sup>2</sup> -   9x -  9</u>
                                             24x<sup>2</sup> +  36x + 17

Now we write the final answer as

                     remainder
         quotient + ——————————— 
                      divisor

                        24x<sup>2</sup> + 36x + 17
        1.5x + .5 + ——————————————————————
                     2x<sup>3</sup> + 2x<sup>2</sup> - 18x - 18

Edwin</pre>