SOLUTION: Use synthetic division and the remainder theorem to find the value of the given function f(-3)=answer formula is : f(x)=x^4+3x^2+5

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Question 628062: Use synthetic division and the remainder theorem to find the value of the given function
f(-3)=answer
formula is : f(x)=x^4+3x^2+5
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x4 + 3x2 + 5

Synthetic division

To do synthetic division with this polynomial you must insert
zero placeholders for the missing 3rd and 1st powers of x.
of x:

f(x) = x4 + 0x3 + 3x2 + 0x + 5

-3|1  0  3   0   5
  |  -3  9 -36 108
   1 -3 12 -36 113

Answer: f(-3) = 113

Check by direct substitution:

f(x) = x4 + 3x2 + 5

f(-3) = (-3)4 + 3(-3)2 + 5

f(-3) = 81 + 3·9 + 5 = 81 + 27 + 5 = 113

So it checks.  The remainder when using a number with synthetic division
will always give the same answer as substituting that number for x directly.

Edwin