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This solution deals with other factorizations.
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x6" was replaced by "x^6".
Step 1 :
Equation at the end of step 1 :
40 - 5x6
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
40 - 5x6 = -5 • (x6 - 8)
Trying to factor as a Difference of Squares :
3.2 Factoring: x6 - 8
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 : 8 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = x6 - 8
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 1 and the Trailing Constant is -8.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,8
Let us test ....
Polynomial Roots Calculator found no rational roots
Final result :
-5 • (x6 - 8)