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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{(x^4-256)/(x-4)}}}      Log On


   

Question 402283: %28x%5E4-256%29%2F%28x-4%29
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E4-256%29%2F%28x-4%29

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:

%28x%5E4-256%29%2F%28x-4%29


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:

%28x%5E4-256%29%2F%28x-4%29

%28%28x%5E2-16%29%28x%5E2%2B16%29%29%2F%28x-4%29

%28%28x-4%29%28x%2B4%29%28x%5E2%2B16%29%29%2F%28x-4%29

%28cross%28%28x-4%29%29%28x%2B4%29%28x%5E2%2B16%29%29%2Fcross%28%28x-4%29%29
  
(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