Simplify the expression, show all of your work 18 : 2x3 / 5-2

2⋅(x  3  −5)

      5

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".  

STEP

1

:

           x3

Simplify   ——

           5  

Equation at the end of step

1

:

      x3      

 (2 • ——) -  2

      5      

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

        2     2 • 5

   2 =  —  =  —————

        1       5  

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       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    

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  2x3 - 10  =   2 • (x3 - 5)  

Trying to factor as a Difference of Cubes:

3.2      Factoring:  x3 - 5  

Theory : A difference of two perfect cubes,  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 :  5  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Polynomial Roots Calculator :

3.3    Find roots (zeroes) of :       F(x) = x3 - 5

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  -5.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,5

Let us test

 P    Q    P/Q    F(P/Q)    Divisor

     -1       1        -1.00        -6.00      

     -5       1        -5.00        -130.00      

     1       1        1.00        -4.00      

     5       1        5.00        120.00      

Polynomial Roots Calculator found no rational roots

Final result :

 2 • (x3 - 5)

 ————————————

      5      

the least common denominator is 40

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: