SOLUTION: Use synthetic division to find the function values. f(x)=x^4-16 find f(1-√2) I know how to work this out with single numbers but I am at a loss when it is like this.

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Question 789685: Use synthetic division to find the function values.
f(x)=x^4-16 find f(1-√2)
I know how to work this out with single numbers but I am at a loss when it is like this.
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Excuse me for handling your question like this:
but, did you mean, "polynomial division", or did you mean as you said, synthetic division? Either way, the process will be messy.

To use regular polynomial division, you would use as dividend, and as divisor.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
f(x)=x4-16 find f(1-√2) 

The best way is by the remainder theorem using synthetic division:

Write x4-16 as  x4+0x3+0x2+x-16 


1-√2|1  0    0     0     -16
    |                               
     1  


1-√2|1  0    0     0     -16
    |   1-√2                        
     1  1-√2 

Multiply (1-√2)(1-√2) = 1-2√2+2 = 3-2√2

1-√2|1  0    0     0     -16
    |   1-√2 3-2√2                  
     1  1-√2 3-2√2  

Multiply (3-2√2)(1-√2) = 3-5√2+2·2 = 3-5√2+4 = 7-5√2

1-√2|1  0    0     0     -16
    |   1-√2 3-2√2 7-5√2            
     1  1-√2 3-2√2 7-5√2      

Multiply (7-5√2)(1-√2) = 7-12√2+5·2 = 7-12√2+10 = 17-12√2


1-√2|1  0    0     0     -16
    |   1-√2 3-2√2 7-5√2  17-12√2   
     1  1-√2 3-2√2 7-5√2   1-12√2

Answer:  1-12√2 

Edwin
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