Question 402283
{{{(x^4-256)/(x-4)}}}
<pre><font face = "batangche" color = "indigo" size = 4><b>
Three ways to do it:

Method 1:  Long division:

     <u>       x³ +  4x² + 16x +  64</u>
x - 4)x<sup>4</sup> + 0x³ +  0x² +  0x - 256
      <u>x<sup>4</sup> - 4x³</u>
           4x³ +  0x²  
           <u>4x³ - 16x²</u>
                 16x² +  0x
                 <u>16x² - 64x</u>
                        64x - 256
                        <u>64x - 256</u>
                                0

The solution is

x³ +  4x² + 16x +  64

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Method 2:  Synthetic division:

{{{(x^4-256)/(x-4)}}}


4 | 1   0   0   0  -256
  |<u>     4  16  64   256</u> 
    1   4  16  64     0

The solution is

x³ +  4x² + 16x +  64

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Method 3:  Factoring and canceling:

{{{(x^4-256)/(x-4)}}}

{{{((x^2-16)(x^2+16))/(x-4)}}}

{{{((x-4)(x+4)(x^2+16))/(x-4)}}}

{{{(cross((x-4))(x+4)(x^2+16))/cross((x-4))}}}
  
(x+4)(x²+16)

You can leave it like that or multiply it out using FOIL:

x³ + 16x + 4x² + 64

or in descending order:

x³ + 4x² + 16x + 64, same answer as when using the long division method.

Edwin</pre>