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