Answer:
Step-by-step explanation: 1.1      Factoring:  343-x6 
Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)
Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 =
         A2 - B2
Note :  AB = BA is the commutative property of multiplication.
Note :  - AB + AB equals zero and is therefore eliminated from the expression.
Check :  343  is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Polynomial Roots Calculator :
 1.2    Find roots (zeroes) of :       F(x) = -x6+343
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient
In this case, the Leading Coefficient is  343  and the Trailing Constant is  -1.
 The factor(s) are:
of the Leading Coefficient :  1,7 ,49 ,343
 of the Trailing Constant :  1
 Let us test ....
  	P    Q    P/Q    F(P/Q)    	Divisor
      -1       1        -1.00        342.00    	
      -1       7        -0.14        343.00    	
      -1       49        -0.02        343.00    	
      -1       343        -0.00        343.00    	
      1       1        1.00        342.00    	
      1       7        0.14        343.00    	
      1       49        0.02        343.00    	
      1       343        0.00        343.00    	
Polynomial Roots Calculator found no rational roots
Final result :
  343 - x6