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.

Algebra ->  Polynomials-and-rational-expressions -> 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.      Log On


   

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) About Me  (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 x%5E4%2B0x%5E3%2B0x%5E2%2B0x-16 as dividend, and x-1%2Bsqrt%282%29 as divisor.

Answer by Edwin McCravy(20060) About Me  (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