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

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Question 402283:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!


Three ways to do it:

Method 1:  Long division:

            x³ +  4x² + 16x +  64
x - 4)x4 + 0x³ +  0x² +  0x - 256
      x4 - 4x³
           4x³ +  0x²  
           4x³ - 16x²
                 16x² +  0x
                 16x² - 64x
                        64x - 256
                        64x - 256
                                0

The solution is

x³ +  4x² + 16x +  64

------------------------------------------------

Method 2:  Synthetic division:




4 | 1   0   0   0  -256
  |     4  16  64   256 
    1   4  16  64     0

The solution is

x³ +  4x² + 16x +  64

------------------------------------

Method 3:  Factoring and canceling:








  
(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
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