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What are the possible rational roots of f(x) = x4 -7x + 8?

 If f(x) = x8 - 1 is divided by x -2, the remainder would be?
 
The zeroes of f(x) = x2 – 8x + 17 are?

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Mark M. | Math Tutor--High School/College levelsMath Tutor--High School/College levels
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By the Remainder Theorem, if f(x) is divided by x-2, the remainder is f(2).
 
   So, remainder = f(2) = (2)8 - 1 = 127
 
By the Rational Zero Theorem, if p/q is a rational zero of a polynomial function, then p is a divisor of the constant term and q is a divisor of the leading coefficient.  
 
  So, if p/q is a rational root of f(x) = x4-7x +8, then p = ±1, ±2, ±4,or ±8 and q = ±1.
 
   Possible rational roots:  ±1, ±2, ±4, ±8
 
   However, I don't think that any of the possibilities is actually a root.  So, the roots are either irrational or complex.