2⋅(x  3  −5)
   5
Â
Step-by-step explanation: I hope this really help!
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x3"  was replaced by  "x^3". Â
STEP
1
:
      x3
Simplify  ——
      5 Â
Equation at the end of step
1
:
   x3   Â
 (2 • ——) -  2
   5   Â
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Â Subtracting a whole from a fraction
Rewrite the whole as a fraction using  5  as the denominator :
    2   2 • 5
  2 =  —  =  —————
    1    5 Â
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Â Â Â Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2x3 - (2 • 5)   2x3 - 10
—————————————  =  ————————
   5        5  Â
STEP
3
:
Pulling out like terms
3.1 Â Â Pull out like factors :
 2x3 - 10  =  2 • (x3 - 5) Â
Trying to factor as a Difference of Cubes:
3.2 Â Â Â Factoring: Â x3 - 5 Â
Theory : A difference of two perfect cubes, Â a3 - b3 can be factored into
       (a-b) • (a2 +ab +b2)
Proof :  (a-b)•(a2+ab+b2) =
      a3+a2b+ab2-ba2-b2a-b3 =
      a3+(a2b-ba2)+(ab2-b2a)-b3 =
      a3+0+0+b3 =
      a3+b3
Check : Â 5 Â is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Polynomial Roots Calculator :
3.3 Â Â Find roots (zeroes) of : Â Â Â F(x) = x3 - 5
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which  F(x)=0 Â
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  -5.
The factor(s) are:
of the Leading Coefficient : Â 1
of the Trailing Constant : Â 1 ,5
Let us test
 P   Q   P/Q   F(P/Q)   Divisor
   -1    1     -1.00     -6.00   Â
   -5    1     -5.00     -130.00   Â
   1    1     1.00     -4.00   Â
   5    1     5.00     120.00   Â
Polynomial Roots Calculator found no rational roots
Final result :
 2 • (x3 - 5)
 ————————————
   5   Â